The robbery and attack was reported at about 5:30 a.m. near McAllister and Webster streets.
The 71-year-old woman was approached by a male suspect who tried to steal her purse. After a struggle, the suspect punched the woman, causing brain bleeding, a contusion and lacerations to her face, police said.
She was taken to San Francisco General Hospital to be treated for the injuries, which are considered life-threatening, according to police.
The suspect fled with the purse and had not been found as of Thursday morning, police said.
Anyone with information about the case is asked to call the Police Department's anonymous tip line at (415) 575-4444 or to send a tip by text message to TIP411 with "SFPD" in the message.