The attack was reported at about 12:30 p.m. Sunday near the intersection of Third Street and McKinnon Avenue, where a food drive was being set up.
Volunteers were stacking food on tables and preparing to give it out when the woman walked ahead of other people in line, then began to take food from the table, according to police.
One of the volunteers asked her to put the food down but she refused, prompting another volunteer to get involved and try to get the woman away from the tables.
At that point, the woman apparently became enraged and pushed the two volunteers, then took out a razor blade and began swinging it at them, cutting one in the arm, police said.
Police responded and arrested the woman, whose name was not immediately available this afternoon. She was booked into jail on suspicion of aggravated assault with a weapon, according to police.
The victim who was sliced was taken to San Francisco General Hospital to be treated for her injury.