The 94-year-old woman was assaulted shortly before 4:45 p.m. Saturday as she crossed the street at the intersection of Stockton and Sacramento streets, according to police.
A man described as about 50 years old came up behind her and, for no apparent reason, punched her several times in the head, police said.
The woman fell and hit her head, and was taken to San Francisco General Hospital for a possible skull fracture and injuries that are considered life-threatening, police said.
The suspect had not been arrested as of this morning, according to police.
Anyone with information about the attack is encouraged to call the Police Department's anonymous tip line at (415) 575-4444 or send a tip by text message to TIP411.