A 24-year-old Bangladeshi woman has been remanded in custody after appearing in court charged over what police allege was an "Islamic State-inspired attack" following a stabbing incident at Mill Park, in Melbourne's north on Friday.

WARNING: Contains an image that may offend some readers.

Police allege the woman, identified as Momena Shoma, is a Bangladeshi national who travelled to Melbourne on February 1 on a student visa and was renting a room in the home of a man identified by neighbours as a 56-year-old nurse.

She was charged with one count of engaging in an act of terrorism and was remanded in custody. She did not make any application for bail.

Police were called to a home in Callistemon Rise about 4:20pm on Friday where they found the man with neck and shoulder injuries after being stabbed while he was asleep.

The man was stabbed while he was asleep in his house on Callistemon Rise, Mill Park, police said. ( ABC News: Danielle Bonica )

The man underwent surgery and is in a serious but stable condition.

His young daughter was present at the time but was not injured.

A neighbour heard a commotion and went to the man's assistance.

Neighbours said Ms Shoma had arrived the day before the incident and had planned to stay for about 10 days.

Police said she had been enrolling in a course at La Trobe University and that it was understood she was wearing a black burqa.

Victoria Police Acting Deputy Commissioner Ross Guenther appealed to the community not to retaliate.

A blood-stained plastic garden chair was outside the home after the attack. ( ABC News )

"We're confident this person acted alone and it was an inspired attack by a person who had become radicalised over a period of time," he said.

"We have evidence that supports that contention which will later be brought before the court.

"We have a well-established Bangladeshi community and we strongly advise that we don't want any retaliatory action against that community because as part of our broader social fabric they're very important to the health of this city of Melbourne."

Charge carries life prison term

Ian McCartney, the acting Australian Federal Police Deputy Commissioner, said police were not looking for anyone else in connection with the incident.

Ian McCartney (left) and Ross Guenther (right) said the charges against the woman were "extremely serious." ( ABC News: Simon Winter )

"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're treating the matter as extremely serious reflected by the fact that the charge in relation to this matter is a maximum penalty of life imprisonment."

The issue of how she became radicalised would be the subject of an international and domestic investigation, Acting Deputy Commissioner McCartney said.

Acting Deputy Commissioner Guenther assured the community it was an "isolated incident".

"The community can expect to see an increased police presence at a number of events today and at major events in the coming weeks," he said.

'Sad, bizarre incident'

In a statement, the family of the injured man thanked family and friends for their support and kindness.

"This is a very upsetting time and we ask that our privacy is respected to allow time to heal," the family said.

"At this time our focus is on our the welfare of our family and his recovery."

Neighbour Neil Fitzroy said the injured man and his family were the first ones to welcome them to the neighbourhood and were engaging and open, which is why they took in overseas homestay students.

"It's extremely sad for a family that was so keen to give people an Australian experience and so welcoming to so many students, that something as terrible can happen through nothing other than generosity and seeking to open their home," he said.

"I think this is a shock to everybody."

He said it would not change how he felt about the neighbourhood.

"I think this is an rather bizarre and isolated incident. It certainly makes me feel no different about this area of Melbourne," he said.

"It's just a really sad incident."

Since September 2014, when the national terrorism threat level was raised, police have charged 85 people, including this woman, following 36 counter-terrorism operations around Australia.