The 67-year-old woman was struck shortly before 3:25 p.m. at California Street and 10th Avenue, police Sgt. Eric O'Neal said.
Fire department spokeswoman Mindy Talmadge said the woman was initially awake and alert following the collision, but O'Neal said she was then taken to San Francisco General Hospital and her injuries are considered life-threatening.
The driver of the car that struck her remained at the scene, O'Neal said.
Streets were blocked in the area and San Francisco Municipal Railway's 1-California bus line was affected by the collision, police said.
The collision is the second in San Francisco Thursday involving a pedestrian and one of several in recent weeks. There were 21 pedestrian deaths in the city last year, the most since 2007.
San Francisco city officials have made pedestrian safety a priority in the new year.
Multiple agencies have held hearings on the issue and adopted "Vision Zero," a list of policies recommended by pedestrian and bicyclist advocates who aim to eliminate traffic deaths in San Francisco over the next several years.
Police Chief Greg Suhr said Wednesday that his department has also stepped up enforcement on city streets. He said traffic citations in January were up 43 percent compared to a year ago.