President Mnangagwa visited the injured at hospitals where they were admitted.
The elections on July 30 will be the first since 1980 - the year the country gained independence from white minority rule - that Mugabe is not in the running.
President Mnangagwa came into power last November after he ousted Robert Mugabe from office.
Those hurt included two vice-presidents, the Zanu-PF party chairwoman, members of a state TV crew and security personnel.
Injured Zanu-PF supporters were pictured in a nearby hospital, where one man wearing a blood-stained party T-shirt waited for treatment. There have been frequent allegations of assassination attempts directed at Mnangagwa and other senior politicians, though none of these have involved bombings or firearms.
"In news just received Vice President Kembo Mohadi, Oppah Muchinguri-Kashiri the Zanu- PF chairperson and political commissar Engelbert Rugeje were injured in the explosion", Zimbabwe Broadcasting Corporation (ZBC) said.
Zimbabwe's main opposition leader, Nelson Chamisa, condemned the attack.
The vote will be a key test for Mnangagwa, 75, who succeeded the 94-year-old autocrat and remains untested at the ballot box.
Mnangagwa adopted most of Mugabe's security and bureaucratic system, fearing a complete overhaul, which the military had sought, could cause instability in government and likely cost him votes.
Witnesses said several people were injured, including the Vice-President.
"While we await further information, my thoughts and prayers are with all those affected by this senseless act of violence".