The fire broke out at about 5:30 a.m. on the eighth floor of an apartment building at 888 O'Farrell St., police and fire officials said.
According to police, a 35-year-old man sleeping in the apartment woke up to find himself and the bed on fire, and ran from the room.
A woman in the apartment then apparently jumped from the window, hitting a tree during the fall, and died, police said.
Police spokesman Sgt. Troy Dangerfield said today the incident was domestic violence-related and is considered a case of arson, attempted murder and suicide. He said police would not be releasing further information.
The woman's name has not been released.
Investigators believe the fire began on the mattress inside the apartment.
It was extinguished a short time later by the apartment's sprinkler system, fire spokeswoman Lt. Mindy Talmadge said. Damage to the apartment has been estimated at $30,000.
The man remains in the hospital and is expected to survive, police said.