This comes amid allegations of identity theft against the deputy.
Messerschmidt fell out with fellow MEP and former party ally, Rikke Karlsson, who last week reported him to the police in Denmark for identity theft in relation to Messerschmidt's administration of an EU grant-receiving foundation.
Karlsson accused Messerschmidt of using her name on official documents without her knowledge.
Karlsson said she was named without her consent to the board of a pan-European party called Movement for a Europe of Liberties and Democracy (MELD) at a 2014 meeting at which she allegedly wasn't present. MELD is now defunct.
The announcement from Messerschmidt came the same day as Karlsson asked the European Parliament to reopen its investigations into MELD's finances under Messerschmidt's leadership.
Earlier this year, the European Parliament ordered Messerschmidt to repay a sum of EU funds, thought to be €400,000, that he allegedly syphoned off on political campaigning in Denmark and on a "golden handshake" to a party consultant.
Messerschmidt is one of three Danish People's Party MEPs.
He is a member of Parliament's constitutional affairs committee and the special committee on tax rulings and other measures similar in nature or effect.
On Thursday, Messerschmidt was reported as saying, "I no longer feel I am the right person to be in charge. Therefore, I accept the consequences and resign as leader of the Danish People's Party in the European Parliament."
Messerschmidt, known in the Danish media as "Teflon Man", will remain as a Vice-Chair and chief whip of the ECR group, according to his spokesperson.
The spokesperson has said the accusations against Messerschmidt are "politically motivated and unsubstantiated."
Following Danish press coverage of the case, a second MEP has come forward to claim that he too did not consent to his name being forwarded to the board of Movement for a Europe of Liberties and Democracy.
Jørn Dohrmann, also a Danish People's Party member, was reported as saying, "I am completely baffled but I do not believe it is legal to put people on a board without their knowledge."
An ECR group spokesman said, "We take note of Messerschmidt's decision while he resolves this matter with the Danish authorities."