The fire at 1550 Filbert St. was reported about 9:30 p.m. Video posted on social media showed smoke and flames coming from the roof of the structure.
The fatality was found on the third floor of the building, fire Rescue Capt. Samuel Menchaca said.
One person was treated at the scene. Firefighters rescued two dogs from the conflagration.
A total of 22 firefighting apparatus and 66 firefighters were dispatched to the fire, Menchaca said.
Stay with ABC7 News for the latest details on this developing story.