The 18-year-old victim was attacked around 5:50 p.m. on a Muni bus in the area of Mission and Valencia streets near Bernal Heights, according to police.
Three suspects had approached the victim and asked her a question, and when she replied, one slashed her across the face with the knife, police said.
The suspects, two men and a woman believed to be in their 20s, fled from the bus and had not been found as of this morning, according to police.
The victim was taken to San Francisco General Hospital to be treated for her injuries, which are not considered life-threatening, police said.
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.