A 24-year-old woman has been charged with allegedly engaging in an 'Islamic State inspired' terrorist act after stabbing a man in the neck as he slept in his Melbourne home.

Momena Shoma, a Bangladeshi national, allegedly attacked the 56-year-old father at his Callistemon Rise home in Mill Park, southeast Melbourne, on Friday afternoon.

He was taken to the Royal Melbourne Hospital where he underwent surgery on Saturday for non-life threatening injuries.

The man's five-year-old daughter was also present during the stabbing but was not injured.

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Momena Shoma, a Bangladeshi national, allegedly attacked the 56-year-old man at his Callistemon Rise home (pictured) in Mill Park, southeast Melbourne, on Friday afternoon

Police arrested the 24-year-old woman following the alleged stabbing (Pictured is a chair from the Melbourne home)

Shoma has been remanded in custody and did not apply for bail when she faced Melbourne Magistrates' Court on Saturday. Pictured: Court sketch of Shoma

Neighbours told Herald Sun the victim was a 'nice family man' and was a 'nice guy'.

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 horrified family of the man have spoken out after the alleged stabbing.

'At this time our focus is on our the welfare of our family and his recovery. We would like to offer our thanks to our family, friendly neighbours and emergency services for their support and kindness,' they said in a statement.

'This is a very upsetting time and we ask that our privacy is respected to allow time to heal.'

The Bangladeshi national was arrested at the Melbourne home where she had been staying while studying

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.

Ian McCartney, AFP acting Deputy Commissioner, National Security, confirmed the incident was linked to Islamic State (Victoria Police stock pictured)

'We will allege this was a stand-alone, Islamic State inspired attack, designed to cause harm to our community,' acting Deputy Commissioner McCartney said (Stock image)

The woman has been remanded in custody and did not apply for bail when she faced Melbourne Magistrates' Court on Saturday.

The magistrate heard Shoma - who faced court in a blue jumper with her hair tied back - injured her left hand during the alleged attack, 9 News reported.

She is expected back in court on May 2.

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.