The shooting was reported at 11:22 a.m. in the 900 block of Market Street.
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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
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