Witnesses told The Associated Press news agency that the blast occurred as Mnangagwa had just finished addressing the crowd and was leaving the podium.
Zimbabwe's president says the explosive device in an attack on his campaign rally went off a "few inches away from me, but it is not my time".
Bulawayo has always been a bastion of opposition to the ZANU-PF and it was Mnangagwa's first rally in the city.
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The Zimbabwe Herald newspaper calls it an attempt on Mnangagwa's life.
Mnangagwa came to power last November, ousting his former mentor Robert Mugabe. "Four security personnel and some chiefs were also injured so all in all we are talking of 8 or 9 people who have been injured", Presidential spokesman George Charamba said.
Mnangagwa said the injured included Vice President Kembo Mohadi, the wife of Vice President Constantino Chiwenga, the environment minister and the deputy speaker of parliament.
He later visited his two injured vice presidents and declared the "cowardly act" will not disrupt elections.
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State broadcaster ZBC also reported that the ZANU-PF party secretary in charge of political organisation, Engelbert Rugeje, was injured.
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. Mnangagwa, a former justice and defense minister who served for decades as Mugabe's enforcer, has invited Western election observers for the first time in nearly two decades.
The US Embassy in Harare condemned the attack.
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