MDC leader Nelson Chamisa says he has evidence to show that he was cheated out of the 30 July presidential vote.
His party says the poll was marred by “mammoth theft and fraud”, but the electoral commission insists that there was “no skulduggery”.
Mr Mnangagwa won 50.8% of the vote compared with Mr Chamisa’s 44.3%.
“The inauguration is no longer going ahead [on Sunday] as planned,” Justice Minister Ziyambi Ziyambi said, after the opposition filed the challenge on Friday.
The Constitutional Court will have 14 days to rule on the MDC Alliances’s legal challenge.
The party must prove that any irregularities were grave enough to change the outcome of the vote. If it does this successfully, the court could order a recount or nullify the result altogether.
Mr Chamisa wants the court to declare him the winner or call a fresh election, his lawyer told Reuters news agency.
“We have a good case and cause!” he tweeted shortly after filing the challenge.
At least six people were killed two days after the vote in clashes between security forces and MDC Alliance supporters who alleged that Mr Chamisa had been robbed of victory.
There was great optimism that the elections would bring real change after the end of Robert Mugabe’s 37-year rule in November.
But the MDC Alliance say the security forces have launched a brutal crackdown on the opposition following the disputed poll.
Mr Mnangagwa has appealed for peace and promised an independent investigation into the post-election violence.
By narrowly winning more than 50% of the vote Mr Mnangagwa avoided a run-off election against Mr Chamisa.
The challenge to the election result comes one day after MDC Alliance politician Tendai Biti appeared in court on charges of inciting violence.
Zambia’s government rejected Mr Biti’s request for asylum, and on Thursday he was released on $5,000 (£4,300) bail and ordered to surrender his passport.
Prosecutors accuse him of fuelling illegal protests by rejecting Mr Mnangagwa’s victory in the fiercely contested elections.
Mr Biti is the first senior opposition politician to be detained since Mr Mnangagwa took over from Mr Mugabe.Post published in: Featured