The Constitutional Court will have 14 days to make a ruling on the legal challenge.
There was great optimism that the elections would bring real change after the end of Robert Mugabe's 37-year rule in November.
Justice Minister Ziyambi Ziyambi told Reuters Sunday's inauguration "will no longer happen" until the case is finalised. "We are seeking a declaration to the effect that the presidential election was not properly conducted", MDC party lawyer Thanbani Mpofu said.
On Thursday, opposition figure Tendai Biti was detained by Zimbabwean police after Zambian authorities rejected his bid for asylum. On Wednesday, General Sibusiso Moyo (Foreign Affairs) sent a circular to diplomatic missions stationed in Zimbabwe inviting their officers to attend Mnangagwa's in inauguration at the national sports stadium.
The outspoken politician was further barred from making any public political statement and to report twice a day at CID law and order division until the court ruled otherwise.
It's amusing that Chamisa (MDC Alliance presidential candidate Nelson) entered an election wanting to win only.
The president-elect who is to be sworn into office this weekend and his party, Zanu-PF, have welcomed the court action. "But if they want to meet us in court we have sufficient legal minds to meet them squarely in court", ZANU-PF legal secretary Paul Mangwana said.
He said those who lost should accept the results and work hard to improve next time.
The election passed off relatively smoothly but its aftermath revealed the deep rifts in Zimbabwean society.
Two days after the vote, six people were killed in an army crackdown on protests against the victory by Mnangagwa's ruling ZANU-PF party, a reminder that Zimbabwe will struggle to fix its image as a nation known for repression and economic collapse.
I am deeply concerned by the violence and human rights violations which have taken place in Zimbabwe since last week's elections.