The bus carrying 21 passengers swerved off the road on Thursday when a front tyre burst, and crashed into a crowd sheltering from the heat under a tree in Udubo village, in the Bauchi state.
Police spokesman Ahmed Mohammed Wakil said in a statement that "the vehicle burst into flames with twenty-one passengers on board (all) burnt beyond recognition".
Four bystanders, including a policeman, sustained serious injuries and were taken to hospital, he added. The policeman later died.
Accidents are common on Nigeria's poorly maintained roads largely due to speeding and a disregard for traffic rules.
Nigeria has seen a sharp rise in road accidents for six consecutive years, with around 42,000 annual deaths, accounting for 2.82 percent of global road fatalities, according to World Bank figures.
Nigeria Bus Crash Kills 22
KANO, NIGERIA - A bus leaves as smoke is seen at a bus park in Abuja, Nigeria, February 1, 2017.