The government says the army was deployed in central Harare to help police restore order.
The opposition MDC Alliance condemned the crackdown, saying it was a reminder of the “dark days” of Robert Mugabe’s rule.
It alleges that the governing Zanu-PF party has rigged Monday’s elections.
Parliamentary results show Zanu-PF heading for a big majority in the first elections since long-serving ruler Mr Mugabe was ousted from power.
The presidential result has yet to be declared. However, the MDC Alliance insists that its presidential candidate, Nelson Chamisa, won Monday’s election.
European Union monitors have expressed concern over the length of time it is taking to declare the presidential result.
The Zimbabwe Electoral Commission (Zec) has announced 140 seats for Zanu-PF so far, and 58 for the MDC Alliance, ZBC state media reported. There are 210 seats in the National Assembly’s lower house.
More than five million people were registered to vote, and there was a high turnout of 70%.