The shooting was reported at 11:22 a.m. in the 900 block of Market Street.
The man shot by police died, and Scott did not have any information on the condition of the stabbing victim.
The police chief did not release any other details about what led to the shooting.
"Loss of life is tragic, doesn't matter how it happens, it's tragic," Scott said. "These things, we try to avoid them as much as we can, but we have an obligation to protect the public."
Market Street is shut down this afternoon as a result of the police investigation, and all San Francisco Municipal Railway buses are being re-routed to other streets. Muni officials advised riders to use subway service while downtown as an alternative.
Lyanne Melendez will have the full story on ABC7 News starting at 4 p.m. Click here to follow her updates on Twitter
Update: Two #SFPD Ofc. were walking on the 900 blk of Market St. They observed a white male subject stabbing an Asian or Filipino male...— San Francisco Police (@SFPD) May 3, 2017
...#SFPD Ofc. intervened. At least one Ofc. discharged a firearm. The victim who was stabbed was transported to a hospital for treatment...— San Francisco Police (@SFPD) May 3, 2017
The Dept. of Police Accountability; & the Medical Examiner's Office.This is preliminary information & remains an active & ongoing inv. #SFPD— San Francisco Police (@SFPD) May 3, 2017
UPDATE: Market bus reroutes as follows: IB: Mkt-8th-Mission-3rd-Market. OB: 4th-Miss.-9th-Mkt. Recommend #subwaysvc 4 IB travel.— SFMTA (@sfmta_muni) May 3, 2017