The Houston Fire Department arrived to flames and smoke coming from the door and stairway that goes to four apartment units.
Firefighters rescued four people who were trapped because that entry was the only way in and out of those apartments.
One child and one adult were transported to the hospital for smoke inhalation, but no major injuries were reported, officials said.
The blaze burned the entry way, stairs and door, but did not make it into any of the units.
According to HFD, someone poured a flammable substance on the stairs and lit the fire.
Investigators said they have had a rash of fires that were intentionally set at the entrances of buildings over the last couple months.