Witnesses said the blast occurred as Mnangagwa had just finished addressing the crowd and was leaving the podium.
Bulawayo has always been seen as a bastion of opposition to the ZANU-PF and it was Mnangagwa's first rally in the city.
Mr Charamba said the 75-year-old president, who was accompanied by his two deputies, was safe at a state house in the city.
Mnangagwa suggested he was the target of the attack, which he said also injured Vice-President Kemo Mohadi.
Presidential spokesman George Charamba told The Zimbabwe Herald that investigations were underway, and pointed out that there have been "multiple attempts" on Mnangagwa's life over the years.
The events in November that brought Mnangagwa into power were driven by deep divisions in the ruling ZANU-PF party, with different factions vying to take over after the nonagenarian Mugabe eventually relinquished power or died. He added: "I can assure you these are my normal enemies".
Mnangagwa on Saturday evening appealed to the southern African nation for unity.
Speaking hours after the explosion, the president said: "The campaign so far has been conducted in a free and peaceful environment and we will not allow this cowardly act to get in our way as we move towards elections". "Our thoughts and prayers go out to the victims and their families", the embassy said in a message posted on Twitter.
"Political violence of any nature from any quarter is totally unacceptable".
The United States and Britain were among countries that condemned the explosion.
Mnangagwa also visited injured people in hospital alongside Chiwenga.
"They will observe the entire electoral process prior, during and after the harmonised elections, scheduled for July 30". So fart he hard-fough campaign has seen little of the violence associated with previous elections in Zimbabwe.
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