The twin-turboprop Beechcraft King Air plane suffered engine failure and crashed into the mall near the end of the runway at Essendon Airport, Victoria state police Assistant Commissioner Stephen Leane told reporters in Melbourne.
Witnesses told Australian Associated Press the plane exploded on impact.
"There were five people on the aeroplane and it looks like nobody's survived the crash," Leane said.
The crash happened at around 9 am, about an hour before the mall was due to open and there were no fatalities other than those aboard the aircraft, he added.
Police did not release information about the identity of the casualties.
The plane had been bound for King Island in Bass Strait between the mainland and the southern island state of Tasmania.
A spokesperson for Airservices Australia said flights in and out of Melbourne's main airport were unaffected. Essendon Airport, which is used mainly by light aircraft, remained closed.
The Australian Transport Safety Bureau will investigate the crash.