A man who ran from the scene has been taken into custody, police said in a statement. There is no ongoing threat to people in Sydney, said New South Wales state Police Minister Yasmin Catley, Reuters reported.
Police said no one was killed in the attack, which came after a "domestic-related" incident in a car that collided with another vehicle in the southern suburb of Engadine.
The attacker "was armed with what we believe to be a boxcutter," police superintendent Donald Faulds said in a televised press conference.
Aerial footage of the scene by the Australian Broadcasting Corp showed two crashed cars cordoned off with police tape.
Sydney, a city of 5 million, has seen a spate of knife attacks this year, prompting the New South Wales government to toughen its knife laws. The state parliament passed laws in June giving police electronic metal-detecting scanners to check people without a warrant at shopping centers, sporting venues and public transport stations.
In April, six people were killed and 12 injured in a knife attack at a mall in Sydney's Bondi area.