The incident happened at about 4:50 p.m. near Third Street and Paul Avenue.
The suspect, a man in his 20s whose name has not yet been released, was involved in an earlier stabbing nearby, according to police.
Police have released scant details about the incident. However, a video posted to Instagram, apparently filmed by a bystander, appears to show a man limping on the sidewalk and surrounded by police officers.
WARNING: Some may find the video below graphic in nature
In the video, someone urges the man to "just drop it," then seconds later a number of shots ring out.
The officer-involved shooting comes as the San Francisco Police Commission was considering policies Wednesday evening for body-worn cameras by the Police Department's officers.
The cameras, not yet worn by officers, are slated to be deployed in San Francisco sometime in 2016.