A photographer from the AFP news agency said the man died at the scene in Harare after being shot in the stomach.
Soldiers arrived after police got into running battles with protesters, who threw stones and burned tyres.
Witnesses said an army helicopter was flying above the country’s capital.
Sky News correspondent John Sparks said tear gas had been used to disperse protesters. Water cannon has also been deployed.
One protester, Norest Kemvo, said he was “beaten by soldiers” after making a “peaceful protest”.
“This is our government,” he said. “This is exactly why we wanted change. They are stealing our election.”
President Emmerson Mnangagwa has called for calm.
“We must all demonstrate patience and maturity, and act in a way that puts our people and their safety first,” Mr Mnangagwa tweeted.
Zanu-PF has won two thirds of seats in parliament, enabling it to change the country’s constitution.
Led by Mr Mnangagwa, Zanu-PF took most rural constituencies, according to official results, while the opposition MDC achieved victories in urban areas.
MDC leader Nelson Chamisa tweeted that he won the “popular vote” in the presidential election.
The country’s electoral commission had been expected to announce the result of the presidential election from 11.30 UK time on Wednesday, but it is not now expected until Thursday.
Mr Mnangagwa promised a free and fair vote and invited international observers.
But according to observers from the EU, the elections were beset by problems with media bias, voter intimidation, and mistrust in the country’s electoral commission.
At some stages. the commission had appeared to be one-sided, the EU’s chief observer, Elmar Brok, said.
This election has been the first ballot since Robert Mugabe was ousted after 37 years in power.
Mr Mugabe voted in the capital, Harare, alongside his wife Grace, following a surprise news conference in which he called on supporters to reject ZANU-PF, his former party.
Mr Mnangagwa faces an unemployment crisis following the collapse of agriculture.
Other concerns include hyperinflation and an exodus of investment.
The results of Zimbabwe’s presidential race – between Mr Mnangagwa and opposition leader Nelson Chamisa – will be announced after all votes have been counted, the electoral commission said.