The incident occurred on Monday, April 17, at the Alaka Bridge, very close to the National Stadium in Surulere.
It is not clear exactly how many people were on the bus, but witnesses said there were passengers who could not be rescued due to the intensity of the fire.
It was also gathered that the wounded victims have been taken to an undisclosed hospital.
In another accident in the Gbagada area of Lagos, two persons lost their lives in an auto crash which involved a commercial bus and a taxi.
A statement by the Lagos State Emergency Management Agency (LASEMA) said the bodies have been moved to the Lagos Mainland Hospital Mortuary.
The agency added that emergency responders also rescued 14 other persons who sustained various degrees of injuries.