It added that several people were said to have been injured but that the extent of the injuries had not yet been established.
The polls in five weeks will be the first since Zimbabwe's veteran leader Robert Mugabe resigned following a brief military takeover in November last year after 37 years in power.
A source close to the president told TimesLIVE that Mnangagwa was "safe".
Meanwhile, the Zimbabwe Red Cross Society (ZRCS) said it had joined other emergency response units that rendered first aid to the injured before ferrying them to hospitals.
The president has joked about the attempts on his life while on the campaign trail.
The president was in Bulawayo to campaign ahead of nationwide elections due on 30 July.
Shock footage shows President Mnangagwa waving to supporters as the alleged bomb went off in the second city of Bulawayo.
Presidential spokesperson Mr George Charamba told the Herald that most of the injured people have been attended to and discharged.
No groups have come forward to say that they were behind the explosion so far.
Although Mnangagwa pleaded for unity and peace after he survived the blast, Eldred Masunungure, a political analyst and academic, expressed scepticism about the possibility of a peaceful election next month.
Officials said Mr Mnangagwa was whisked from the stadium rally to a nearby government building in Bulawayo, a traditional opposition stronghold.
That dramatic transfer of power began when Mr Mnangagwa was sacked as Mr Mugabe's deputy and said he had to immediately flee the country for his life.
"This sours the political environment after it seemed like all parties were taking steps to ensure the election would be free of violence".
Western countries say a credible vote is key to lifting sanctions.
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