Exhibit 5.1

AbbVie Inc.

1 North Waukegan Rd.

North Chicago, Illinois 60044

Ladies and Gentlemen:

We have acted as special counsel to AbbVie Inc., a Delaware corporation (the “Company”), in connection with the issuance and sale by the Company of $1,250,000,000 in aggregate principal amount of the Company’s 4.650% Senior Notes due 2028 (the “2028 Notes”), $1,000,000,000 in aggregate principal amount of the Company’s 4.875% Senior Notes due 2030 (the “2030 Notes”), $1,000,000,000 in aggregate principal amount of the Company’s 5.200% Senior Notes due 2035 (the “2035 Notes”) and $750,000,000 in aggregate principal amount of the Company’s 5.600% Senior Notes due 2055 (the “2055 Notes” and, together with the 2028 Notes, the 2030 Notes and the 2035 Notes, the “Notes”). The Notes were sold pursuant to an Underwriting Agreement, dated February 18, 2025, by and among the Company and BofA Securities, Inc., J.P. Morgan Securities LLC, Morgan Stanley & Co. LLC, Barclays Capital Inc. and Mizuho Securities USA LLC, acting for themselves and as representatives of the several Underwriters named therein (the “Underwriting Agreement”). The Notes are to be issued under that certain Indenture, dated as of November 8, 2012, between the Company and U.S. Bank Trust Company, National Association, as successor-in-interest U.S. Bank National Association, as trustee (the “Trustee”), as supplemented by that certain Supplemental Indenture No. 11, dated as of February 26, 2025, between the Company and the Trustee (collectively, the “Indenture”).

AbbVie Inc.

February 26, 2025

Page 2

We have examined and relied on originals or copies certified or otherwise identified to our satisfaction of such documents, corporate records, certificates of the Company and public officials and other instruments as we have deemed necessary or appropriate for the purposes of this letter, including (a) the registration statement on Form S-3ASR (File No. 333-284980), filed with the Securities and Exchange Commission (the “Commission”) on February 14, 2025 (the “Registration Statement”), but excluding the documents incorporated therein; (b) the base prospectus, dated February 14, 2025, included in the Registration Statement, but excluding the documents incorporated therein; (c) the preliminary prospectus supplement, dated February 18, 2025, as filed with the Commission pursuant to Rule 424(b)(5) under the Securities Act of 1933, as amended (the “Act”), but excluding the documents incorporated by reference therein; (d) the final term sheet dated February 18, 2025, as filed with the Commission pursuant to Rule 433 under the Act; (e) the prospectus supplement, dated February 18, 2025, as filed with the Commission pursuant to Rule 424(b)(5) under the Act, but excluding the documents incorporated by reference therein; (f) a copy of the Amended and Restated Certificate of Incorporation of the Company and a copy of the Third Amended and Restated Bylaws of the Company, each as set forth in the certificate of the Secretary of the Company, dated the date hereof; (g) the Indenture; (h) a copy of the Global Notes for each series of the Notes, each dated as of February 26, 2025; (i) an executed copy of the Underwriting Agreement; (j) resolutions of the Board of Directors of the Company relating to the issuance of the Notes; and (k) such other corporate records, certificates and other documents and such matters of law, in each case, as we have deemed necessary or appropriate. In such examination, we have assumed (i) the authenticity of original documents and the genuineness of all signatures; (ii) the conformity to the originals of all documents submitted to us as copies; (iii) the truth, accuracy and completeness of the information, representations and warranties contained in the agreements, records, documents, instruments and certificates we have reviewed; (iv) all Notes will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the Prospectus Supplement; and (v) the Underwriting Agreement has been duly authorized and validly executed and delivered by the Underwriters. We have assumed that the terms of the Notes have been established so as not to, and that the execution and delivery by the parties thereto and the performance of such parties’ obligations under the Notes will not, breach, contravene, violate, conflict with or constitute a default under (1) any law, rule or regulation to which any party thereto is subject (excepting the laws of the State of New York as such laws apply to the Company); (2) any judicial or regulatory order or decree of any governmental authority; or (3) any consent, approval, license, authorization or validation of, or filing, recording or registration with any governmental authority. We also have assumed that the Indenture and the Notes are the valid and legally binding obligation of the Trustee. As to any facts material to the opinion expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others. We have further assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, facsimile, conformed, electronic or photostatic copies, and the authenticity of the originals of such copies.

We are members of the Bar of the State of New York, and we have not considered, and we express no opinion as to, the laws of any jurisdiction other than the laws of the State of New York in effect on the date hereof.

Based upon the foregoing, and subject to the assumptions, limitations, qualifications, exceptions and comments set forth in this letter, we advise you that, in our opinion, the Notes, when duly executed, authenticated, issued, delivered and paid for in accordance with the terms of the Indenture and the Underwriting Agreement, will be valid and binding obligations of the Company, enforceable against the Company in accordance with their terms

AbbVie Inc.

February 26, 2025

Page 3

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally; (b) general equitable principles (whether considered in a proceeding in equity or at law); (c) an implied covenant of good faith and fair dealing; (d) provisions of law that require that a judgment for money damages rendered by a court in the United States be expressed only in United States dollars; (e) limitations by any governmental authority that limit, delay or prohibit the making of payments outside the United States; and (f) generally applicable laws that (i) provide for the enforcement of oral waivers or modifications where a material change of position in reliance thereon has occurred or provide that a course of performance may operate as a waiver, (ii) limit the availability of a remedy under certain circumstances where another remedy has been elected, (iii) limit the enforceability of provisions releasing, exculpating or exempting a party from, or requiring indemnification of a party for, liability for its own action or inaction, to the extent the action or inaction involves negligence, gross negligence, recklessness, willful misconduct or unlawful conduct, (iv) may, where less than all of a contract may be unenforceable, limit the enforceability of the balance of the contract to circumstances in which the unenforceable portion is not an essential part of the agreed-upon exchange, (v) may limit the enforceability of provisions providing for compounded interest, imposing increased interest rates or late payment charges upon delinquency in payment or default or providing for liquidated damages or for premiums upon acceleration, or (vi) limit the waiver of rights under usury laws. Furthermore, the manner in which any particular issue relating to the opinions would be treated in any actual court case would depend in part on facts and circumstances particular to the case and would also depend on how the court involved chose to exercise the wide discretionary authority generally available to it. We express no opinion as to the effect of Section 210(p) of the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010, as amended.

We express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof, including, without limitation, the enforceability of the governing law provisions contained in the Notes and the Indenture. We express no opinion as to the ability of another court, federal or state, to accept jurisdiction and/or venue in the event the chosen court is unavailable for any reason, including, without limitation, natural disaster, act of God, human health or safety reasons or otherwise (including a pandemic).

This letter speaks only as of its date and is delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act. We hereby consent to the filing of a copy of this letter as an exhibit to the Company’s Current Report on Form 8-K, filed on February 26, 2025, and to the use of our name in the prospectus forming a part of the Registration Statement under the caption “Validity of the Securities.” In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act.