A police spokesman said the rampage broke out in Cronulla late on Monday, the same beach-side suburb where a night of race riots resulted in scores of arrests on Sunday, and in neighbouring Caringbah.
Paul Bugden, a spokesman for New South Wales police, said: "We have shops damaged at Caringbah, cars damaged at Cronulla. We have six arrests at this stage."
One person was apparently hit with a stone outside the Cronulla police station, he added, saying that youths in cars were involved in the violence.
The Australian Associated Press reported that gunshots were heard near Cronulla beach, but police could not confirm the report.
Bugden said he did not have descriptions of those involved in Monday night's rampage, but the rioting on Sunday involved mostly white males shouting racist chants aimed at those of a Middle Eastern appearance.
The Australian Associated Press, citing a resident who declined to be named, said men riding in up to 50 cars and wielding baseball bats converged on Cronulla, smashing cars.
Ambulances were called to help at least one injured man seen lying on the side of the road.