The fight was reported at 12:58 a.m. in the 1700 block of Post Street.
Officers responded to find the three victims -- two men ages 25 and 28 and a 25-year-old woman -- who had been struck in the head with beer bottles, according to police.
The victims were taken to San Francisco General Hospital to be treated for bruising to the face and head, police said. All are expected to survive.
About 15 people believed to be involved in the brawl all had fled before officers arrived and have not been found.
Anyone with information about the case is encouraged to call the Police Department's anonymous tip line at (415) 575-4444 or send a tip by text message to TIP411.