George Charamba told Reuters the 75-year-old president, who was accompanied by his two deputies, was unhurt and taken to safety after the blast on Saturday.
"There has been an incident at Bulawayo (White City Stadium) where the president was addressing a rally. This is now a police issue, but the president is safe at Bulawayo State House," the spokesman said, Presstv Reported.
He added, "We are still to get information on what exactly happened as we understand that some people could have been injured as this happened in the VIP tent."
Footage from Zimbabwe’s state television showed that the explosion took place near the president as he waved to supporters.
Images broadcast on Zimbabwean TV also showed scenes of chaos and medics fighting to save those injured in the explosion in the country's second city Bulawayo.
Zimbabwe said in late May it would choose a new president and parliament on July 30, in the country's first electoral test since the removal of its former leader Robert Mugabe.
"Monday, the 30th day of July, 2018 (is) the day of the election to the office of President, the election of members of the National Assembly and election of councilors," Mnangagwa said in a proclamation on May 30.
Once a right-hand man to the 94-year-old Mugabe, Mnangagwa succeeded the veteran leader, who had been nearly four decades in charge, in November after troops swarmed the streets and briefly seized key sites.
Mnangagwa, will square off against the main opposition Movement for Democratic Change (MDC) party, now led by 40-year-old Nelson Chamisa following the death of Morgan Tsvangirai in February.