Police say it happened while the man was crossing 7th Street at Mission Street just after 8 a.m. The victim appears to be in his 60's.
The bus driver remained at the scene, and has cooperated with police.
Investigators are trying to figure out who was at fault for the accident.
The bus company, Gray Line of San Francisco, released a statement Sunday night. Besides the driver, they say there were three guests aboard the bus at the time. They say they're cooperating with officials and that it may take several days for authorities to review all the info.
"Our company, Gray Line of San Francisco has been in business for 26 years with a perfect safety record, to my knowledge this is the first incident as such," said Paul Nakamoto with Gray Line. "The driver involved has been with our company for a number of years and his driver's record is clean. The motorcoach involved also has a clean safety record. Of course our first concern is for those involved."