Mr Mnangagwa said an object “exploded a few inches away from me – but it is not my time”.
Video footage from White City Stadium shows an explosion happening close to Mr Mnangagwa as he leaves the stage after addressing supporters.
Health Minister David Parirenyatwa said 15 people were injured, three of them seriously.
The exact number of people hurt by the blast remains unclear – and reports suggest it may be significantly higher.
The president was in Bulawayo, Zimbabwe’s second city and an opposition stronghold, to campaign for his Zanu-PF party ahead of nationwide elections taking place on 30 July.
He is favourite to win the poll, but analysts say he also has enemies – both for overthrowing his former mentor, Robert Mugabe, and for being a previous enforcer of the Mugabe regime.
A spokesman for Mr Mnangagwa said that while the president was unhurt, Vice-President Kembo Mohadi suffered a leg injury. Another vice-president, Constantino Chiwenga, received bruises to his face.
Other officials, including Zanu-PF party chairwoman Oppah Muchinguri-Kashiri, were also injured, as were some crew members from state broadcaster ZBC and security personnel.
Mr Mnangagwa, 75, said he had visited the injured in hospital. He condemned the violence as senseless and pleaded for unity.
“I am used to these attempts,” he told state media.
Mr Mnangagwa came to power last November after ousting Mr Mugabe.
He was evacuated from the scene soon after the blast.
“People started running in all directions and then immediately the president’s motorcade left at a very high speed,” an AFP news agency correspondent at the scene reported.
The elections are the first in Zimbabwe since Mr Mugabe was forced out after 37 years in power.
“Vice-President Mohadi is nursing some leg injuries but he is in good spirit,” he was quoted as saying.
Marry Chiwenga, the wife of Vice-President Chiwenga, was also injured and pictures on social media showed the president visiting her in hospital.
Opposition leader Nelson Chamisa condemned the attack.
“Political violence of any nature from any quarter is totally unacceptable,” he said.
“In the past 38 years political violence has been a permanent feature and an anticipated ritual… which we must expunge.”
The election – dominated by economic issues – is the first to be monitored by international observers since 2002. Mr Mnangagwa has said the vote will be free and fair.