"At this stage the advice we have is there are no fatalities other than on the aircraft itself," said Victoria Police Assistant Commissioner Stephen Leane.
The charter flight appeared to have had "catastrophic engine failure" on take-off from Melbourne's small Essendon Airport, he said.
The centre was not open at the time.
Victoria's Police Minister Lisa Neville said the five people were travelling to Tasmania's King Island, in nearby Bass Strait.
"It appears to be a very, very tragic accident that has occurred out there," she told the Australian Broadcasting Corp.
A spokeswoman for Spotlight, a retailer in the complex, said the plane crashed into its rear warehouse but all staff were safe.
Essendon Airport, mostly used by light planes, is about 13km (8 miles) north-west of central Melbourne.
Damage at scene
The Australian Transport Safety Bureau said it would investigate how the twin-engine Beechcraft B200 King Air crashed soon after 09:00 local time on Tuesday.
Footage broadcast on local media showed fire and black smoke at the wreckage.
"Immediately I could tell it was something horrific, the explosion would have gone 30m [100ft] high and ballooned upwards in red and black," witness Mikey Cahill told the Herald Sun.
Another witness, Daniel May, said he was waiting for the shopping centre to open when the plane came down.
"There was an orange explosion and then smoke," he told The Age. "Emergency crews rushed very quickly in, soon after, and I left the area."
Police said they were evacuating the area and a nearby freeway was closed in both directions.
King Island, popular for its beaches and dairy farms, lies 245km (150 miles) south of Melbourne in Bass Strait.