By soon after midday, downtown Harare was largely empty.
On Wednesday, Mnangagwa said Friday's protest would constitute an "insurrection" by the opposition.
A police statement said no demonstrations would be allowed on Friday. "All security arms of government are on full alert and will deal decisively with any individuals or groups fomenting violence and sending threats or provocative messages through the social media or any other means," it said.
Soldiers manned checkpoints on roads leading into the city centre, with vehicles turned back.
Critics say Mnangagwa, like other authoritarian leaders round the world, is exploiting the coronavirus lockdown to stifle dissent.
Illustrating the crisis, senior doctors at government hospitals said they had stopped work on Thursday over poor conditions, joining thousands of nurses who quit work last month to press for U.S. dollar salaries.
Seven babies were stillborn in one night at a major hospital this week because their mothers did not get adequate medical care due to the nurses' strike.