The stabbing was reported at about 2:15 a.m. near Sixth and Natoma streets.
The 21-year-old victim was heavily intoxicated and was unable to provide investigators with detailed information about the attack, according to police.
He was taken to San Francisco General Hospital to be treated for his injuries, which are not considered life-threatening.
No arrests had been made in connection with the slashing as of this morning. 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.