Pictures emerged on social media of Mnangagwa standing next to a hospital bed where one of his vice presidents' wife, Mary Chiwenga, is receiving treatment.
Mr Mnangagwa, who has joked about multiple attempts on his life, said he was used to them by now.
Mr Mnangagwa, 75, said he had visited the injured in hospital. The strongest response to violence is peace.
The Zimbabwe Herald newspaper reported that Vice-President Kembo Mohadi had suffered leg injuries in the bomb blast, but there is no confirmation.
In a message posted on his Facebook wall soon after the incident, Mnangagwa said: "Let us continue to be united and address our differences peacefully".
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Zimbabwe's presidential candidates are not normally provided with security by the government.
In the past, the President has himself openly joked about the attempts, including during his campaigning. "I have scars on account of political violence in the past, so it's something we have budgeted for", he said in an interview held on the lawns of a hotel in Kadoma now hosting opposition and ruling party members alike.
The Zimbabwe Republic Police (ZRP) has offered a substantial reward following the explosion which occured at Bulawayo's White City Stadium on Saturday. She said investigations are underway and appealed to anyone with information to contact the Criminal Investigations Department.
"Mrs Chiwenga was slightly injured".
"Our prayers go out to the injured and we hope no lives have be lost", Chamisa said.