The 32-year-old man allegedly confronted officers called to Chisholm Street in Darlinghurst about 4.40pm on Sunday.
"The man allegedly approached officers and NSW Ambulance paramedics whilst armed, before a constable discharged their firearm," NSW Police said in a statement.
"The man was treated at the scene before being taken to St Vincent's Hospital in a stable condition."Police said a critical incident team from a different police area command would investigate the incident, which would be subject to an independent review.
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