The attack was reported shortly after 5 p.m. in the 1100 block of Market Street, between Sixth and Seventh streets.
The 57-year-old man confronted the woman, who was damaging the mural with the knife. She then turned around and slashed the man's face, then ran away, according to police. She had not been found as of this morning.
The victim was taken to St. Francis Memorial Hospital to be treated for his injuries, which are not considered life-threatening.
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.