The incident was reported at 2:18 p.m. at Eddy and Leavenworth streets.
San Francisco fire spokeswoman Mindy Talmadge said the victim was struck by a transport van and pinned underneath the vehicle.
Fire crews responded and extricated the victim at 2:38 p.m., she said.
Two ambulances were called -- one for the pedestrian and another for the driver, who began suffering from a medical problem.
Talmadge said she did not yet have details about how the accident occurred. Police spokesman Officer Albie Esparza said the accident shut down a stretch of Eddy Street.