The two-alarm fire was reported at 9:50 a.m. Wednesday at a three-story building at 65 Cleary Court, located near Laguna Street.
The blaze started in an apartment on the second floor and spread to a third-story unit, according to fire department spokeswoman Mindy Talmadge.
Watts, a San Francisco resident, was in an apartment on the second floor, Talmadge said.
Two other men suffered smoke inhalation from the fire but declined to be taken to a hospital, while one firefighter suffered a minor laceration, according to Talmadge.
She said the cause of the blaze remains under investigation.