Rasoul Al Mousawi, 47, was blasted with a shotgun in the face and shoulder in a drive-by shooting outside the Husainiyah Nabi Akram Centre in suburban Greenacre early yesterday.
Police said his wounds were not life threatening.
A witness, who declined to be identified, told Australian Broadcasting Corp that men in the car had driven past the centre several times before the shooting, calling out "IS lives forever" and "Shia dogs."
Prime Minister Tony Abbott confirmed that authorities suspected the Islamic State movement was behind the shooting. "It seems there is an ISIL death cult influence on this shooting in Sydney in the last 24 hours or so," Abbott told reporters.
The government also blames the Islamic State movement for a violent encounter in the city of Melbourne in September in which an 18-year-old terror suspect was shot dead after he stabbed two policemen. Neither officer was killed.
Counterterrorism teams have raided homes in Sydney, Melbourne and Brisbane, Australia's three largest cities, in recent months and have charged several people with terrorism-related offences.