The 40-year-old opposition chief lost the July 30 polls to Mnanagagwa but Chamisa has held hat he has evidence to show that he was cheated out of the presidential election.
His party says the poll was marred by "mammoth theft and fraud", but the electoral commission insists that there was "no skulduggery".
By narrowly winning more than 50% of the vote Mr Mnangagwa avoided a run-off election against Mr Chamisa. "For now it has been stayed pending determination of the court challenge", Zimbabwe's Justice Minister Ziyambi Ziyambi, said.
Under the constitution, a losing presidential candidate has seven days to challenge the result from when a victor is declared.
The Constitutional Court, which can declare a new victor or order a fresh election, must rule within 14 days of an election petition. If it does this successfully, the court could order a recount or nullify the result altogether.
Also on Friday, lawyers for senior opposition figure Tendai Biti asked judges to throw out charges against him over the protests against alleged election fraud, in a case raising further global concern about the new government. We have a good case and cause!
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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.
"After 37 years in power, (former) president Robert Mugabe's resignation heralds the beginning of a new era in Zimbabwe, not only symbolically, but also in terms of the country's prospects for meaningful economic reform", BMI said in January.
The United States has criticised the treatment of opposition supporters and in particular key opposition figure Tendai Biti, who has been arrested in connection with the post-election violence.
The electoral commission declared the Zanu-PF's Emmerson Mnangagwa had 50.8% of votes against the MDC Alliance's Nelson Chamisa's 44.3%.
Zimbabwe Movement for Democratic Change (MDC) Alliance official Tendai Biti was released on $5,000 bail by a court in Harare on Thursday evening.
Prosecutors accuse him of fuelling illegal protests by rejecting Mr Mnangagwa's victory in the fiercely contested elections.
Zambia risks losing aid from the USA government following the forced deportation of Zimbabwean opposition politician Tendai Biti.