The MDC-T lawyer Chris Mhike served the withdrawal affidavits at the ConCourt in Harare this evening (Friday).
The MDC-T says that without information such as the number of people not on the voters' roll who voted, it cannot prove that the elections were fraudulent.
The arguments in the MDC-T's legal challenge were due to begin on Saturday.
But MDC spokesman Douglas Mwonzora said that, without the extra information, the challenge "was going to be a mockery of justice", reports the AFP news agency.
The withdrawal of its challenge paves the way for Mr Mugabe, 89, to be inaugurated for another five-year term.
He has governed Zimbabwe since independence in 1980.
Meanwhile, former MDC-T's legislator for Mount Pleasant constituency, Mr Jameson Timba's request for a recount of ballots in the constituency has been dismissed by the Electoral Court on the basis of lack of merit.
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