Mr Chamisa tweeted: "Our legal team successfully filed our court papers".
The MDC-Alliance intends to scuttle the inauguration through an application challenging the presidential election results.
Analysts say that the legal challenge has little chance of success given the courts' historic tilt towards ZANU-PF, which has ruled since independence from British colonial rule in 1980.
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.
There will still be a core European Union team to monitor the election petitions in the urgent, and no doubt fiercely fought, court days ahead.
Mr Mnangagwa won 50.8% of the vote, compared with Mr Chamisa's 44.3%, in the 30 July poll, the first since Robert Mugabe was ousted after 37 years as president in November.
"We've managed to place before the court forms that show the (results) figures were erased. 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.
"The inauguration is no longer going ahead (on Sunday) as planned", Justice Minister Ziyambi Ziyambi told AFP.
The aftermath of the election has been marred by allegations of a crackdown on opposition members, including beatings and arrests.
It said it had received numerous complaints of intimidation, often by men in military uniform, of voters thought to have backed the opposition.
Diplomats and election observers were present at the court hearing in Harare after Biti fled to Zambia but was handed back to Zimbabwean police despite claiming asylum.
Tendai Biti was released earlier today following my intervention.
"The ZHRC has established that there is hunting down and harassment of polling agents for independent candidates and opposition political parties", it said.
In the days following the poll, six opposition supporters died in clashes with the army, which has led some to question about its neutrality.
"On the basis of the evidence we have placed before the court, we seek in the main relief to the effect that the court should declare the proper victor and the proper victor is my client", Mpofu told reporters outside.