The Houston Fire Department said crews responded to the incident just before 2 p.m. at Westhollow Place along Richmond Avenue.
HPD said the fire was upgraded to a 2-alarm fire about 15 minutes later before a "mayday" call was issued.
A firefighter doing a search on the property reportedly fell from a second-floor level after a balcony collapsed.
Officials said the firefighter was taken to Memorial Hermann-Texas Medical Center and suffered non-life-threatening injuries.
It's still unclear what started the fire or if anyone else was injured.