Dramatic footage captured from the scene shows officers try to apprehend the man following his stabbing attack.
They attended the Virgin Mary Mosque in Hoppers Crossing, west of Melbourne.
The assailant had a minor criminal history of drug, theft and driving offences, and he lived in a suburb of Melbourne northwest of the city.
Police have said they believe the attacker acted alone and they are not searching for other suspects.
A strong police presence is at both properties in Werribee and Meadow Heights.
A 24-year-old man from Hampton Park and a 58-year-old Launceston man, said to be Tasmanian businessman Rod Patterson, were taken to hospital with non-life threatening injuries.
While it was known he held radicalised views, federal police didn't believe he posed a serious threat, and revealed he was not being actively monitored at the time of the attack.
The Islamic State group has claimed responsibility for the attack.
The spokesperson advised a "small number of people" have been stabbed and police are not seeking anyone further at this time.
The suspect drove to the Bourke Street area at around 4.10pm yesterday and deliberately started a fire in his vehicle before fleeing it.
The man was shot after confronting police officers on a busy city street, authorities said. He has been arrested and taken to hospital in a critical condition.
"He's someone that was known to us", Ashton said.
"We need to be ruthless and relentless against people who are going commit this sort of violence in whatever twisted, perverse definition of religion or ideology makes them to this".
On Saturday, as investigators searched the family home, carloads of distressed relatives arrived at the house only to be turned away by heavily armed police guarding the driveway.
Mr Ashton said police were "doing security reassessments of these events in light of what's occurred", but there was "no ongoing threat we're now aware of in relation to people surrounding this individual".
Businesses are now shut near the incident, with police telling people to stay inside.
One of the officers eventually shot him in the chest.
"But we also thank the police who did us proud in very unsafe circumstances".
The victims' identities have not be made public, but Ashton said all three, including the deceased, are men.
Victoria's opposition leader, Matthew Guy also denounced the attack.
"Here in Australia, we would be kidding ourselves if we did not call out the fact that the greatest threat of religious extremism in this country is the radical and unsafe ideology of extremist Islam", he said.
"All the resources of our state should be directed towards keeping Victorians safe".
Authorities say Australia's vigilance has helped to foil at least a dozen plots, including a plan to attack downtown Melbourne at Christmas in 2016.
"For operational matters we now have the counter-terrorism command and the homicide squad dealing with this matter, and there are ongoing investigations being conducted by the counter-terrorism command", he continued.
"Australians will never be intimidated by these appalling attacks and we will continue to go about our lives and enjoy the freedoms that the terrorists detest", Morrison declared.
He added: "These are traumatic events, they are terrifying. This is Victoria Police, please evacuate the area".
"Our thoughts are with everybody affected, including family and friends".
"I didn't know what was happening there was just so much chaos and screaming".
"We need to understand and become familiar with risks and hazards".