Victoria Police said officers "initially responded to a report of a auto on fire" in the city center at around 4:20pm local time, as people began to leave work for the weekend.
Another witness on a passing tram told ABC Radio it seemed police had been trying to subdue a man who was waving something.
Mobile phone footage shows a man, wielding a weapon, attacking officers about 4.20pm. See the videos below.
Three people were stabbed in the incident and authorities have confirmed one of those victims has died.
"Police shot the male and he is now in a critical condition and under guard in hospital".
Videos from the scene showed officers arresting the man on the sidewalk immediately after he was shot.
"Three people have been stabbed, unfortunately one is deceased at the scene, two other victims are now in hospital".
Another person at the scene said: "I saw people running, screaming".
The two surviving victims are being treated in hosptial. Their condition is not yet know. They are not looking for anyone else.
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The apparent attack came as a 28-year-old James Gargasoulas underwent trial in Melbourne for driving into a crowd in the same area in 2017, killing six people.
No further information was available at the time of writing.
Sarah Werkmeister, a witness, told The Herald Sun: "All I saw was the vehicle on fire, and the police cuffing someone on the ground".
- windix (@windix) November 9, 2018On Bourke St. Roads blocked.
People also told local media that they saw police trying to calm down the attacker. What is this insanity?
One person was arrested and is in a critical condition after he was a shot by police as he lunged at officers with a knife at the busiest Bourke Street mall in Melbourne.
The suspect has been shot and is alive, police say.
Police are urging any witnesses to attend Melbourne West police station to provide a statement, while anyone with vision or photographs from the incident is being urged to upload footage to the Victoria Police Facebook site.
It is normal for people to have strong emotional or physical reactions following a distressing or frightening event.