The confrontation began at 11:30 Friday night on Linden Boulevard in Flatbush.
Police say 19-year-old Stanley Cherenfant threatened them with an 11-inch kitchen knife with a six-inch blade.
Police tried to stop Cherenfant with pepper spray, but it had no effect on him so they shot the suspect once in the abdomen.
Cherenfant was taken to Kings County Hospital where he is listed in stable condition.
Police said an eleven-inch kitchen knife with a six-inch blade was recovered at the scene.
Cherenfant is charged with menacing and criminal possession of a weapon.