The Houston Fire Department responded to the flames at the 10000 block of Club Creek Drive at about 5:16 a.m.
Officials said the fire escalated and damaged 16 units, three of which were occupied. The fire was put out at about 5:47 a.m., the department added.
The Red Cross told ABC13 that four people were displaced due to the fire, and 35 more due to a power outage caused by it. Those displaced are currently staying at St. Matthew's Church.
No one was hurt, and the cause of the fire is under investigation.
Firefighters said a section of this same apartment building had already been on fire at least two other times. Authorities did not provide additional information about those previous fires.