Exhibit 5.1

JONES DAY

SILICON VALLEY OFFICE  •  1755 EMBARCADERO ROAD  •  PALO ALTO, CALIFORNIA 94303

TELEPHONE: +1.650.739.3939 • FACSIMILE: +1.650.739.3900

February 25, 2016

MagnaChip Semiconductor Corporation

c/o MagnaChip Semiconductor S.A.

1, Allée Scheffer, L-2520

Luxembourg, Grand Duchy of Luxembourg

Re: Registration Statement on Form S-8 Filed by MagnaChip Semiconductor Corporation

Ladies and Gentlemen:

We have acted as counsel for MagnaChip Semiconductor Corporation, a Delaware corporation (the “Company”), in connection with the registration under the Securities Act of 1933, as amended (the “Act”), of an aggregate of 691,378 shares (the “Shares”) of common stock, par value $0.01 per share, and the associated stock purchase rights that may be issued to holders of the Shares (the “Rights”), of the Company that may be issued or delivered and sold pursuant to the MagnaChip Semiconductor Corporation 2011 Equity Incentive Plan (the “2011 Plan”). In connection with the opinions expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinions. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that:

1. The Shares that may be issued or delivered and sold pursuant to the 2011 Plan will be, when issued or delivered and sold in accordance with the 2011 Plan and the authorized forms of stock option, restricted stock or other applicable agreements thereunder, validly issued, fully paid and nonassessable, provided that the consideration for the Shares is at least equal to the stated par value thereof.

2. When issued in accordance with the Rights Agreement, dated as of March 5, 2015, between the Company and American Stock Transfer & Trust Company, LLC, as rights agent (as it may be amended from time to time, the “Rights Agreement”), the Rights will constitute valid and binding obligations of the Company.

In rendering the opinions set forth above, we have assumed that the resolutions authorizing the Company to issue or deliver and sell the Shares pursuant to the 2011 Plan and the applicable award agreements will be in full force and effect at all times at which the Shares are issued or delivered or sold by the Company, and that the Company will take no action

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JONES DAY

February 25, 2016

Page 2

inconsistent with such resolutions. In addition, we have assumed that each award under the 2011 Plan will be approved by the Board of Directors of the Company (the “Board of Directors”) or an authorized committee of the Board of Directors.

In rendering the opinion set forth in paragraph 2 above, we have also assumed that (i) the Board of Directors has acted and will act in accordance with its fiduciary duties with respect to the authorization, execution, delivery and administration of the Rights Agreement and the issuance and administration of the Rights and (ii) the Rights Agreement constitutes a valid and binding obligation of each party thereto other than the Company. It should be understood that (x) the Rights, by their terms, are subject under certain circumstances to becoming void in the hands of certain holders or purported transferees, (y) our opinion addresses the Rights and the Rights Agreement in their entirety and does not address the validity or binding effect of any particular provision of the Rights or the Rights Agreement, and (z) the effect, if any, that the invalidity of any particular provision of the Rights Agreement or the Rights might have on any other provision, or the entirety, of the Rights Agreement or the Rights is not settled under applicable law and could be affected by the facts and circumstances existing at the time of any adjudication of the issue. It should also be understood that our opinion does not address the substance or consequences of any determination that a court of competent jurisdiction may make regarding whether the Board of Directors would be required to redeem or terminate, or take other action with respect to, the Rights Agreement or the Rights at some future time based on the facts and circumstances existing at that time.

As to facts material to the opinions and assumptions expressed herein, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others. The opinions expressed herein are limited to the General Corporation Law of the State of Delaware as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement on Form S-8 filed by the Company to effect registration of the Shares to be issued or delivered and sold pursuant to the 2011 Plan under the Act. In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day

Jones Day