All five people on board were killed in the crash, according to a police statement
. The four passengers were from the United States, while the pilot was Australian.
Texan Greg Reynolds De Haven, 70, was among the passengers killed -- his sister Denelle Wicht told CNN De Haven had been going on a golf outing with some friends during a three-week trip to Australia.
"He was an awesome guy," she said, describing him as athletic, a marathoner and a "man's man."
He was also traveling with his wife, who wasn't on board the plane, Wicht said.
De Haven was a retired FBI agent, who had spent 30 years as a member of the agency.
No one was inside the still-closed DFO shopping center when the plane went down around 9 a.m., officials said, but some nearby witnesses were being treated for shock.
"It was a catastrophic plane crash, that has taken a number of lives. But certainly if we look at the circumstances, we've been very lucky today depending on the time of day and who was around," Stephen Leane, Assistant Commissioner of Victoria Police said.
The complex will remain closed for another day, police said.
Lisa Neville, Victoria's Minister for Police, told reporters on the scene that details regarding the cause of the crash "are still being confirmed by police and fire services," CNN affiliate Seven Network reported.
Neville said she believed the plane was a Hawker Beechcraft and said police and firefighters remained at the scene.
She described the crash as a "very tragic accident" and said she expected authorities to have more updates on potential victims shortly.
All flights in and out of Essendon, a smaller airport that is separate from Melbourne Airport, were temporarily suspended. Some portions of the usually packed Tullamarine Freeway were closed earlier on Tuesday due to scattered debris from the crash.
Aerial pictures from Seven Network showed rescue workers on the scene, as well as damage to the roof and infrastructure of the shopping center.
In a post on Twitter, Australian Prime Minister Malcolm Turnbull said he was "deeply saddened" by the accident
"Our hearts and prayers are with the victims and their families," he said.