Exhibit 5.1

12 March 2019

To: Board of Directors

Mallinckrodt plc

College Business & Technology Park

Cruiserath

Blanchardstown

Dublin 15

Ireland

Re: Mallinckrodt plc—Form S-8 Registration Statement

Dear Sirs,

1. Basis of Opinion

We are acting as Irish counsel to Mallinckrodt plc, registered number 522227, a public company limited by shares, incorporated under the laws of Ireland, with its registered office at College Business & Technology Park, Cruiserath, Blanchardstown, Dublin 15, Ireland (the “Company”), in connection with the registration statement on Form S-8 (the “Registration Statement”), to be filed with the United States Securities and Exchange Commission (the “SEC”) on 12 March 2019 under the Securities Act of 1933, as amended (the “Securities Act”) with respect to ordinary shares with a nominal value of US$0.20 per share of the Company (the “Shares”) that may be delivered pursuant to the Mallinckrodt Pharmaceuticals Stock and Incentive Plan (the “Plan”).

1.1 This Opinion is confined to and given in all respects on the basis of the laws of Ireland (meaning Ireland exclusive of Northern Ireland) in force as at the date hereof as currently applied by the courts of Ireland. We have made no investigation of and we express no opinion as to the laws of any other jurisdiction or the effect thereof. This Opinion speaks only as of its date.

1.2 This Opinion is also strictly confined to the matters expressly stated herein at paragraph 2 below and is not to be read as extending by implication or otherwise to any other matter.

1.3 As Irish counsel to the Company in connection with the registration of the Shares, we have examined:

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(a) the documents listed in the schedule (the “Schedule”) to this opinion (the “Documents”);

(b) the searches listed at paragraph 1.5 below; and

(c) such other documents and records as we have deemed necessary to enable us to render the opinions set forth below.

We express no opinion, and make no representation or warranty, as to any matter of fact or in respect of any documents which may exist in relation to the Plan other than the Documents.

1.4 In giving this Opinion, we have examined and relied on copies of the Documents sent to us by email in pdf or other electronic format.

1.5 For the purpose of giving this Opinion, we have caused to be made the following legal searches against the Company on 12 March 2019 :

(a) on the file of the Company maintained by the Irish Registrar of Companies in Dublin for returns of allotments, special resolutions amending the constitution of the Company (the “Constitution”) and notice of the appointment of directors and secretary of the Company and for the appointment of any receiver, examiner or liquidator;

(b) in the Judgments Office of the High Court for unsatisfied judgments, orders, decrees and the like for the twelve years immediately preceding the date of the search; and

(c) in the Central Office of the High Court in Dublin for any proceedings and petitions filed in respect of the Company.

2. Opinion

Subject to the assumptions set out in this Opinion and to any matters not disclosed to us, we are of the opinion that:

2.1 the Company is a public company limited by shares and is duly incorporated and validly existing under the laws of Ireland; and

2.2 when the Shares have been issued pursuant to and in accordance with the terms and conditions referred to or summarised in the applicable resolutions and the Plan, the Shares will be validly issued, fully paid up and non-assessable (which term means when used herein that no further sums are required to be paid by the holders thereof in connection with the issue of such shares).

3. Assumptions

For the purpose of giving this Opinion, we assume the following without any responsibility on our part if any assumption proves to have been untrue as we have not verified independently any assumption:

Registration Statement and the Plan

3.1 that when filed with the SEC, the Registration Statement will not differ in any material respect from the drafts that we have examined;

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3.2 that the Shares will be allotted and issued in the manner stated in the Plan;

3.3 that the Company will receive consideration equal to the aggregate of the nominal value and any premium required to be paid up on the Shares issued pursuant to awards under the Plan and that such consideration will be in cash and/or otherwise provided in accordance with Irish law;

3.4 that the filing of the Registration Statement with the SEC has been authorised by all necessary actions under all applicable laws other than Irish law;

3.5 that the exercise of any options granted under the Plan and the issue of the Shares upon exercise of such options (and the issue of the Shares in connection with any other awards granted under the Plan) will be conducted in accordance with the terms and the procedures described in the Plan and the applicable award agreement;

3.6 that the Company has sufficient share capital to issue the required number of Shares to be delivered to recipients of any awards granted under the Plan and the directors have sufficient authority pursuant to Section 1021 of the Act to issue such Shares, and to the extent applicable, have been authorised to issue such Shares without the application of pre-emption rights pursuant to Section 1023 of the Act;

3.7 that the maximum number of Shares issued pursuant to awards granted under the Plan shall not exceed the amount authorized under resolution 5 approved at the annual general meeting of the Company of May 16, 2018 (“Resolution 5”) or any renewal thereof when aggregated with all other Shares issued pursuant to or in reliance upon, as the case may be, Resolution 5 or the applicable renewal thereof;

3.8 that the maximum number of Shares issued pursuant to awards granted under the Plan to persons that are not employees or former employees of the Company or any subsidiary of the Company shall not exceed the amount authorized under resolution 6 approved at the annual general meeting of the Company of May 16, 2018 (“Resolution 6”, and together with Resolution 5, the “Resolutions”) and any renewal thereof when aggregated with all other Shares issued pursuant to or in reliance upon, as the case may be, Resolution 6 or the applicable renewal thereof;

3.9 with respect to Shares issued pursuant to awards granted on or after the date of expiry of the Resolutions, the Company shall have renewed its authority to issue Shares and dis-apply pre-emption rights on the same terms as the Resolutions (modified only in respect of the extension of the expiry date), and such renewal of the Resolutions shall be in effect at the time of such grant;

Authenticity and bona fides

3.10 the completeness and authenticity of all Documents submitted to us as originals or copies of originals (and in the case of copies, conformity to the originals of such copies), the genuineness of all signatories, stamps and seals thereon and where incomplete Documents have been submitted to us that the originals of such Documents are identical to the last draft of the complete Documents submitted to us;

3.11 that the copies produced to us of minutes of meetings and/or of resolutions correctly record the proceedings at such meetings and/or the subject matter which they purport to record and that any meetings referred to in such copies were duly convened, duly quorate and held, that those present at any such meetings were entitled to attend and vote at the meeting and acted bona fide throughout and that no further resolutions have been passed or other action taken which would or might alter the effectiveness thereof;

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3.12 that there is, at the relevant time of the allotment and issue of the Shares, no matter affecting the authority of the directors to issue and allot the Shares, not disclosed by the Constitution or the resolutions produced to us, which would have any adverse implications in relation to the opinions expressed in this Opinion;

3.13 that the Constitution effective as of 1 March 2017 is the current Constitution, is up to date and has not been amended or superseded and that there are no other terms governing the Shares other than those set out in the Constitution;

Accuracy of searches and warranties

3.14 the accuracy and completeness of the information disclosed in the searches referred to in paragraph 1.5 above and that such information has not since the time of such search or enquiry been altered. It should be noted that searches at the Companies Registration Office, Dublin, do not necessarily reveal whether or not a prior charge has been created or a resolution has been passed or a petition presented or any other action taken for the winding-up of or the appointment of a receiver or an examiner to the Company;

3.15 the truth, completeness and accuracy of all representations and statements as to factual matters contained in the Documents; and

Commercial Benefit

3.16 that the Documents have been entered into for bona fide commercial purposes, on arm’s length terms and for the benefit of each party thereto and are in those parties’ respective commercial interest and for their respective corporate benefit.

4. Disclosure

This Opinion is addressed to you in connection with the registration of the Shares with the SEC. We hereby consent to the inclusion of this Opinion as an exhibit to the Registration Statement. In giving this consent we do not thereby admit that we are in a category of person whose consent is required under Section 7 of the Securities Act.

The opinion is governed by and is to be construed in accordance with the laws of Ireland as interpreted by the courts of Ireland at the date hereof.

Yours faithfully,

/s/ ARTHUR COX

ARTHUR COX

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SCHEDULE

The Documents

1. A copy of the Registration Statement to be filed by the Company with the SEC.

2. A copy of the Plan.

3. A copy of the resolutions of the board of directors of the Company dated February 28 – March 1, 2018 and minutes of the human resources and compensation committee of the board of directors of the Company dated March 21, 2018 approving the Plan.

4. A certificate of the secretary of the Company dated March 11, 2019, including an extract of the resolutions approved by resolutions of the board of directors of the Company dated February 28 – March 1, 2018 and the minutes of the human resources and compensation committee of the board of directors of the Company dated March 21, 2018 regarding the approval of and adoption of, among other things, the Plan and all other matters contemplated thereby and the approval and filing of the Registration Statement with the SEC and certifying the approval of resolution 4, 5 and 6 in the notice of annual general meeting and definitive proxy statement for the 2018 annual general meeting of shareholders filed on April 4, 2018 at the annual general meeting of the Company on May 16, 2018.

5. A copy of the Constitution of the Company effective March 1, 2017.

6. A copy of the Certificate of Incorporation of the Company on registration as public limited company dated 9 January 2013.

7. Letter of status from the Irish Companies Registration Office dated 12 March 2019.

8. A copy of the Company’s notice of annual general meeting and definitive proxy statement for the 2018 annual general meeting of shareholders filed on April 4, 2018.

9. A copy of the final report of the Inspector of Elections in respect of the annual general meeting of the shareholders of the Company dated May 16, 2018.