Another neighbour said the man called them for help, where they found him lying in the garage in a pool of blood.
"I saw all the blood, it was shocking, I saw so much blood," they said.
The woman was arrested at the scene and taken to hospital with a hand injury.
"She's only been in Australia for a week, they took her in because they felt sorry for her," another neighbour said.
She had travelled to Melbourne on February 1 on a student visa and was renting a room at the property while studying at La Trobe University.
Detectives at the scene allege the woman - dressed in a black burka - used a knife to attack the father as his daughter watched on.
How and why the young Bangladeshi woman became radicalised will remain the subject of investigation, police said.
Police also allege the woman was "inspired by the doctrines of ISIS".
The man regularly opened his home to international students and was providing accommodation for the 24-year-old woman.
He remains in hospital in a "serious but stable" condition, police said.
The Victorian JCTT, which is made up of resources from the Australian Federal Police, ASIO and Victoria Police, has charged her with one count of engaging in a terrorist act under the Commonwealth Crimes Act Section 101.1.
Ian McCartney, AFP acting Deputy Commissioner, National Security, confirmed the incident was linked to Islamic State.
"We will allege this was a stand-alone, Islamic State inspired attack, designed to cause harm to our community," acting Deputy Commissioner McCartney said.
"We deplore any attempt to intimidate our community. The AFP will continue to work together with Victoria Police to ensure the safety of the community and to protect our way of life in Australia."
Deputy Commissioner McCartney said there are no subsequent terrorism threats to the community.
The woman has been remanded in custody and will face Melbourne Magistrates' Court on Saturday.
Investigators will be executing search warrants at the Mill Park home and another home in Bundoora, north Melbourne, where the woman had previously stayed.
There is no suggestion that anyone in the Bundoora residence was involved in the incident in any way.
Police are not looking for anyone else in relation to the investigation which they believe was an isolated incident.
"This is an isolated incident and the community can be assured that Victoria Police is doing everything we can to keep the community safe," Acting Deputy Commissioner Ross Guenther said.
"The community can expect to see an increased police presence at a number of events today and at major events in the coming weeks.
"We urge people to report any suspicious activity to triple zero (000), Crime Stoppers on 1800 333 000 or the National Security Hotline on 1800 123 400."
Since 12 September 2014, when the national terrorism threat level was raised, police have charged 85 people – including this woman – as a result of 36 counter terrorism-related operations around Australia.
