The hit-and-run was reported at 12:51 a.m. in the 2100 block of Market Street.
The 39-year-old victim was crossing Market Street when he was struck by the vehicle, which then fled north on Sanchez Street, according to police.
The victim was taken to San Francisco General Hospital to be treated for head injuries that are considered life-threatening, police said.
Neither the hit-and-run vehicle nor driver had been found as of this morning, and police did not immediately have more details about the suspect.
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.