The police department and Suhr have faced mounting criticism and protests for months in the wake of several high-profile police killings and a racist text scandal.
"I have previously expressed confidence in Chief Suhr because I know he agrees with and understands the need for reform," Lee told reporters at a press conference in City Hall. "But following this morning's officer-involved shooting and my meeting with Chief Suhr this afternoon, today I have arrived at a different conclusion to the question of how best to move forward."
San Francisco Police spokeswoman Officer Grace Gatpandan said she could not comment on the resignation. "The statement was given by the mayor. That's all we have," she said.
Hours earlier, Suhr told reporters that around 9:45 a.m. two officers approached a 27-year-old woman as she sat in a car that had been reported as stolen. Neither the woman nor the officers have been identified. Suhr did not give the race of the officers and said he did not know whether the woman was armed.
The woman tried to drive off, crashing into another vehicle fewer than 100 feet away. She was shot by one of the officers, a sergeant, after refusing to comply with their orders, Suhr said. She later died at an area hospital.
Suhr said the officers have not been interviewed.
The use of lethal force by U.S. police, especially by white officers against African-Americans and other minorities, has been the focus of nationwide protests.
Thursday's shooting occurred in San Francisco's Bayview neighborhood, where in December police fatally shot a black man who was a suspect in a stabbing. Police said then that 26-year-old Mario Woods, whose family has sued the city, was holding a knife and refused to drop it.
Bystander video of that shooting, which went viral after being published online, showed Woods being shot in a hail of gunfire by officers. The city's public defender has called the shooting unnecessary.
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