The military swept into the capital Harare to disperse protesters after the Zanu-PF won a parliamentary majority in the vote.
Soldiers opened fire with guns, water cannon and tear gas, as opposition demonstrators burned cars and threw rocks at helicopters hovering above.
Police have invoked a strict security act that forbids public gatherings amid the violence.
The United Nations has urged political leaders and Zimbabweans to reject any form of violence.
Weeping family members have been seen at the Parirenyatwa Hospital in the capital where a man’s body lay on a stretcher.
He has been identified locally as street vendor Ishmeil Kumeni, 42, who was caught in the crossfire.
Brighton Chizhande, chairman of the Zimbabwe Doctors for Human Rights, says the organisation has confirmed one death from a gunshot wound near the heart.
They are following up reports that four others have died.
Mr Chizhande added that the injured include people with deep wounds in the shoulder, buttocks and another suffered a “gunshot wound to the penis”.
President Emmerson Mnangagwa said in a statement that the opposition under Nelson Chamisa was responsible for the disturbance of national peace” meant to “disrupt the electoral process”.
Zimbabwe holds parliamentary and presidential elections separately, with the electoral commission saying the outcome of the latter will be released “sometime tomorrow”.
Both the EU and US observer missions urged the release of the presidential results as soon as possible.
Official results show the ruling Zanu-PF party won the most seats in the parliamentary ballot, but the opposition Movement for Democratic Change (MDC) rejected the outcome and claimed there had been fraud.
The EU observer mission has expressed “serious concerns” as to whether the vote was free and fair – crucial for lifting international sanctions on the once-prosperous country.
The mission said “a truly level playing field was not achieved” in the election, pointing out the “misuse of state resources, instances of coercion and intimidation, partisan behaviour by traditional leaders and overt bias in state media”.
Mr Chamisa, a lawyer and pastor who leads the opposition MDC, has claimed victory based on results supporters said they collected from agents in the field.
He tweeted: “We won the popular vote & will defend it!”
The opposition has also claimed that voting results were not posted outside one-fifth of polling stations as required by law.
The MDC has told reporters that Mr Chamisa was “shocked” by the violence in Harare.
A spokesman said: “We are seriously meant to wonder that this means.
“Are we at war?”
The elections in Zimbabwe are the first since Robert Mugabe was forced out of his presidency last year.