Police arrested Momena Shoma, 24, at the scene after the incident in the city's north on Friday afternoon. The man's young child was present, but not hurt.
"We deplore any attempt to intimidate our community. We will continue to work together with Victoria Police to ensure the safety of the community and to protect our way of life in Australia."
Police said the woman was a Bangladeshi national who travelled to Melbourne on February 1 on a student visa and was renting a room in the 56-year-old's Mill Park home.
A neighbour told the Herald Sun newspaper the man managed to call her and she rushed to his home where she found him in the garage surrounded by a pool of blood.
"I saw all the blood, it was shocking, I saw so much blood," she said.
The Australian Broadcasting Corporation cited police as saying Shoma was wearing a black burqa at the time.
She was charged with one count of engaging in an act of terrorism and remanded in custody when she appeared in court today.
In light of the alleged attack, police said their public presence would be beefed up in coming weeks at major events, including a T20 cricket international between Australia and England.
Since then, 85 people have been charged -- including Shoma -- as a result of 36 counter-terrorism related operations around the country, police said.
At least 14 attacks have been prevented in the past few years, according to authorities, including an alleged plot by an IS-sympathiser to kill as many revellers as possible on New Year's Eve in Melbourne last year.
Despite this, several attacks have taken place, including a cafe siege in Sydney in 2014 where two hostages were killed.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)