"We are treating this as a terrorism incident", Ashton said, and added that the attacker's identity is not being released due to the ongoing investigation.
Investigators believe terrorism is a likely motive. The person is known to police.
Witnesses said the man - who was wearing a dark tunic - attacked members of the public in a popular shopping district with a knife as his vehicle was ablaze, before being confronted by police.
Police did not identify the attacker but Ashton said the man was known to them and intelligence authorities because of family associations.
Footage from the scene shows a man earlier swinging a knife at two uniformed officers near a burning auto before he was shot. He was taken into custody in a critical condition.
UPDATE: The terrorist attacker has since died of his injuries.
Officers were initially called to reports of a auto fire near Bourke Street, a busy thoroughfare, at about 4.20pm local time.More news: Samsung's foldable phone uses 7.3-inch, 4.5-inch screens
Officers were confronted near the burning auto by a man "brandishing a knife and threatening them" while passers-by called out that people had been stabbed, he said.
EARLIER: ONE person is dead after being stabbed in Melbourne's Bourke St this afternoon. He lunged at them with a knife when they got out of the vehicle.
Officers said they "are not looking for anyone further at this early stage". As the attacks continued, one policeman shot the suspect in the chest, leaving him in a critical condition.
Prime Minister Scott Morrison has said Australians will "never be intimidated by these appalling attacks".
Victoria state Premier Daniel Andrews says the attack was "an evil and terrifying thing that has happened in our city and state today". "It certainly wasn't remotely sophisticated, evidenced by the fact that the vehicle just caught fire".
"I'm not in Melbourne now, we got out".
"He seemed to be waving something, people around me screamed that he had a knife, but I couldn't see clearly from where I was", she said.More news: Minnesota, Michigan send first Muslim women to US Congress
Police cordon off Bourke St after a auto explosion.
Hair said the assailant was dressed in Islamic clothing and of African appearance and about six foot four inches tall.
The exploded vehicle was inside a designated pedestrian area.
Any witnesses who caught footage of the incident are also asked to upload their files to the Victoria Police Facebook page.
Another bystander told AAP he was walking on Swanston Street when he heard an explosion and then saw a "big dude punching into the police car". I thought it was like what happened a year ago so I started running.
Islamic State's Amaq news website said in a statement that the man was "one of Islamic State fighters", according to Reuters.
A Somalian man went on a knife rampage in central Melbourne today, stabbing three people after setting a auto full of explosives on fire. He was shot as he tried to stab two officers and died later in Royal Melbourne Hospital.More news: Trump Celebrates 'Beautiful Barbed Wire' On U.S.-Mexico Border