The elderly man answered the knock at his front door on Canterbury Road in Middle Park about 7.50pm on Thursday.
He was shot in the leg and needed to be taken to hospital with non-life threatening injuries.
Two women inside the home, aged 72 and 39, were uninjured.
The offender fled the scene on foot and was last seen heading towards Albert Park Lake.
Police are looking at whether it was a case of mistaken identity.
"It's very brazen, very concerning that someone would do this," Detective Acting Inspector Chris Ellway told reporters on Friday.
"We'll be looking at all avenues of inquiry."
Detectives are yet to arrest anyone in relation to the shooting.
They are instead urging members of the public who witnessed the incident or have dashcam footage to come forward.
"We believe that around that time of night... there would have been people driving past or people walking around the area," Det Act Insp Ellway said.
"They may have seen something - a man in a white hazmat or painter's suit would stand out."
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