One of the officers, a male senior constable, was bitten by a dog during the scuffle and is being treated in hospital.
Police were continuing to scour the residential street, a large section of which had been taped off, and the backyard of one house. An ambulance was in the street and a police riot squad vehicle was parked on the grass opposite homes.
Acacia Avenue is a couple of blocks behind the main St Marys shopping strip on Queen Street. Police are urging members of the public to avoid the area.
NSW Police said in a statement that the shooting was being treated as a critical incident and the homicide squad will investigate the circumstances surrounding the incident. That probe will be subject to an independent review.