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.
What are the two sides saying?
President Emmerson Mnangagwa was quoted by state broadcaster ZBC as saying: "We hold the opposition MDC Alliance and its whole leadership responsible for this disturbance of national peace, which was meant to disrupt the electoral process."
Justice Minister Ziyambi Ziyambi said the army had been deployed in Harare to disperse a violent crowd and to restore "peace and tranquillity".
He added: "The presence of the army is not to intimidate people but to ensure that law and order is maintained. They are there to assist the police."
A spokesman for Mr Chamisa condemned the deployment of soldiers and the subsequent loss of life.
"Soldiers are trained to kill during war. Are civilians enemies of the state?" he asked.
"There is no explanation whatsoever for the brutality that we saw today."
Correspondents say the violence was confined to the centre of Harare - an opposition stronghold - while other parts of the country remain calm. Latest reports from the capital suggest the security forces are in control of the streets.