The "country is peaceful" as Zimbabwe prepares to stage its first ever elections not to feature former president Robert Mugabe on July 30, Mnangagwa says.
Fifteen people were injured, three seriously and some lost limbs, in the explosion during an election campaign event in Zimbabwe's second city Bulawayo, according to Health Minister David Parirenyatwa.
Footage circulating on social media showed an explosion and plumes of smoke around the president as he descended stairs from the podium at the city's White City stadium.
Mnangagwa suggested he was the target of the attack, which he said also injured Vice-Presidents Kembo Mohadi and Constantino Chiwenga.
"I am used to these attempts," Mnangagwa told state media, adding that an object "exploded a few inches away from me -- but it is not my time".
ZANU-PF chairwoman and cabinet minister Oppah Muchinguri-Kashiri and Mary Chiwenga, the wife of vice president Chiwenga, were also among those injured, he said, as was deputy parliament speaker Mabel Chinomona.
The "blast has affected my vice-presidents especially comrade Mohadi," he added.
Mohadi suffered leg injuries, while Chiwenga had slight bruises to his face, according to the presidential spokesman George Charamba.
State broadcaster ZBC described the blast as "an assassination attempt".
According to Charamba, the president was "evacuated successfully" to his official residence in Bulawayo.
"This is going to make everyone a little bit tense, this is the first time we have seen such a blatant attack," she said blaming divisions inside the ruling ZANU-PF for the attack.
"Whatever internal fissures existed within ZANU-PF before (the coup in) November, those fissures didn’t go away."
Twenty-three candidates - the highest number in the country's history -- will contest the presidential race.