The man emerged from a car which then burst into flames, bringing central Melbourne to a standstill in the late afternoon rush.
Officers called to the scene were confronted by a man "brandishing a knife and threatening them" and at the same time passers-by called out that people were stabbed, Victoria State police Superintendent David Clayton said, AP reported.
One person who was stabbed was dead at the scene and two who were injured were taken to a hospital.
Clayton said investigators were looking for no other assailants. The man police shot in the chest was in critical condition.
He said a bomb squad was making the scene safe. "There's no known link to terrorism at this stage. We'll keep an open mind as to whether there's any link," Clayton said.
Victoria police tweeted a request for witnesses to speak to police and share imagery that may assist the investigation.
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