
Michael Rogers, dubbed "Trolley Man" online, was filmed on 9 November trying to prevent Hassan Khalif Shire Ali from stabbing two police officers.
- The suspect had already killed a cafe owner and injured two other people.
- He was later shot by police and died in hospital.
- Mr Rogers was called in by police for questioning on Friday.
Australian media reported that the five alleged offences - two counts of burglary, two counts of theft and committing an indictable offence while on bail - had taken place before the 9 November attack.
Mr Rogers has been hailed as a hero for his efforts to prevent Shire Ali from stabbing two police officers.
When tracked down by reporters, the 46-year-old told 7 News: "I threw the trolley straight at him, and I got him. I didn't quite get him down, though."
At the time he was only metres from a burning car full of gas cylinders, which the attacker had set alight near Bourke Street, a busy road in the city centre.
An online fundraising campaign for Mr Rogers has raised more than A$140,000 ($103,000; £80.000).
It was set up by Donna Stolzenberg, founder of the charity Melbourne Homeless Collective, to help get him back on his feet.