Mr Mnangagwa took power in November after his former ally Mr Mugabe stepped down under military pressure.
Bulawayo, Zimbabwe's second-largest city, is traditionally an opposition stronghold.
Presidential spokesman George Charamba issued a statement recalling: "There have been multiple attempts on the president's life over the past five years".
There are reports that other government officials including VP Kembo Mohadi and Oppah Muchinguri were also taken by paramedics after suffering injuries caused by the bomb blast.
"Four security personnel and some chiefs were also injured so all in all we are talking of 8 or 9 people who have been injured".
President Emmerson Mnangagwa calls on the country for unity despite political differences after "this senseless act of violence".
The president, who survived what is thought to have been an assassination attempt on his life has urged the country to "remain calm and address our differences peacefully".
"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", Mnangagwa said.
The elections are the first in Zimbabwe since Mr Mugabe was ousted after 37 years in power.
Mnangagwa was there campaigning ahead of the nationwide elections taking place next month.
Zimbabwe last had blasts at rallies in the 1980s, which had targeted Mugabe.
For the first time since Zimbabwe gained independence from Britain in 1980, the 94-year-old will not be contesting in the election.
Mnangagwa's rise to the presidency was fiercely resisted by Mugabe loyalists, including his wife Grace.