He later visited his two injured vice presidents and declared the "cowardly act" will not disrupt elections.
"I am used to these attempts", Mnangagwa said in his first comments on the explosion in the country's second city of Bulawayo. The state-run newspaper, the Herald, quickly termed the attack an "assassination attempt".
Marry Chiwenga, the wife of Zimbabwe's First Vice-President, Constantino Chiwenga, was also injured and pictures on social media showed the president visiting her in hospital.
The president's spokesman, George Charamba, released a statement saying Mnangagwa was unhurt and an investigation was underway.
New Zealand PM in hospital to give birth
Government and opposition politicians wished Ardern well, when news broke that she had gone to hospital early this morning. The couple announced at the start of 2018 that they were expecting their first child in June. "It's really exciting.
He succeeded former Zimbabwe President Robert Mugabe after a brief military takeover past year. Zanu-PF is led by Mnangagwa, a former vice-president known as "the Crocodile", who took power when Mugabe was ousted.
He said he was awaiting further information about the blast but added those responsible must have come from "outside Bulawayo".
Mr Mnangagwa on Saturday evening appealed to the southern African nation for unity.
A ZANU PF official tweeted a video clip that he says captured the explosion. Violence must have no place in our politics'.
Alli remains a doubt for Panama clash
Walker said Holland had apologised to the squad at Friday's training session for allowing the picture to be taken. Tunisia like to play the ball out from the back and were very patient but Panama are probably more direct.
State TV immediately cut its broadcast.
The US Embassy in Harare condemned the attack.
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.
Worldwide observers are in the country for the first time since 2002 and, if they endorse the conduct of the ballot, it could help Zimbabwe secure funding from global institutions for the first time in two decades.
Hazard porte la Belgique, la Tunisie pratiquement éliminée — Tops/Flops Belgique-Tunisie
Pour ce match, le sélectionneur belge Roberto Martinez reconduisait le même onze de départ que lors du premier match. A la 41e minute, c'est un autre Tunisien qui va devoir céder sa place, le défenseur central Syam Ben Yousseff.