City police were called to 125 West Washington at just before midnight and found smoke coming from the back of the building. An upstairs tenant was able to put the fire out before firefighters arrived.
Four people were in the upper apartment at the time and one of them suffered an asthma attack from smoke inhalation, but did not require medical treatment.
The building is owned by David Monago.
Anyone with information about this incident is asked to contact City of Bradford Police.