At about 1:40 p.m., an 18-year-old man riding an outbound 14-Mission bus got into an altercation with a 19-year-old man, Muni spokesman Paul Rose said.
The altercation escalated as the bus neared Mission Street and Foote Avenue, and the 19-year-old man stabbed the other man, Rose said.
San Francisco police spokeswoman Lyn Tomioka said the victim suffered multiple stab wounds and was aided by the driver and passengers until emergency medical personnel arrived.
He was transported to a hospital with life-threatening injuries and remained in critical condition this morning, Tomioka said.
The 19-year-old man got off of the bus with a female passenger and both fled on foot, Rose added.
Tomioka said the bus was stopped near the intersection while the driver and witnesses were interviewed.
A camera inside the bus captured video footage of the incident, she added.
"Thousands of people ride Muni each day," Tomioka said. "And this is a very rare incident."
Rose said that Muni employs safety personnel from multiple agencies to prevent crime on the transit system.