A sleeping father was unaware he had been stabbed in the neck until he woke in pain following an alleged 'ISIS-inspired attack' in Melbourne.

Roger Singaravelu, a dedicated nurse, was allegedly stabbed by an international student wearing a burqa at his home in Mill Park, north-east of Melbourne’s CBD, about 4.25pm yesterday.

His five-year-old daughter, who was with him at the time, was not injured.

Roger Singaravelu, a dedicated nurse, was injured while sleeping at his Mill Park home. (Facebook)

Momena Shoma, 24, appeared in a Melbourne court this morning. (9NEWS)

The 56-year-old was taken to the Royal Melbourne Hospital, where he underwent surgery today for non-life-threatening injuries.

The Bangladeshi suspect, identified as Momena Shoma, who recently moved to Australia and held a student visa, was renting a room at Mr Singaravelu's home and was arrested at the scene over the stabbing.

The state's Joint Counter Terrorism Team has charged her with engaging in a terrorist act, under the Commonwealth Crimes Act Section 101.1.

The 24-year-old did not apply for bail when she faced Melbourne Magistrates Court for a brief hearing today.

Mr Singaravelu’s family released a statement today thanking the friend and family for their outpouring of support.

Police were called to a stabbing at Mill Park yesterday. (Twitter / @DougalBeatty)

A 56-year-old man was stabbed in the neck at a Mill Park home. (Twitter / @DougalBeatty)

“At this time our focus is on the welfare of our family and his recovery,” the statement said

“We would like to offer our thanks to our family, friendly neighbours and emergency services for their support and kindness.

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

Ms Shoma, who faced court in a blue jumper with her black hair tied back, suffered an injury to her left hand and will see a nurse in custody, the magistrate heard.

It's alleged Shoma travelled to Melbourne on a student visa on February 1 and was renting a room at the victim's Callistemon Rise home while studying.

She was enrolled in a course at La Trobe University, police said.

Investigators searched the Mill Park home and another property in Bundoora, where she had previously stayed.

Police were not looking for anyone else, Acting Deputy Commissioner Ross Guenther said.

"This is an isolated incident and the community can be assured that Victoria Police is doing everything we can to keep the community safe," he said.

Police have charged a woman with engaging in a terrorist act. (Twitter / @DougalBeatty)

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

There were no subsequent threats to the community, AFP acting Deputy Commissioner, National Security, Ian McCartney said.

"We will allege this was a stand-alone, Islamic State inspired attack, designed to cause harm to our community," he 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."

Police warned Victorian's to expect an increased police presence at events across the city this weekend, although there are not aware of any threats.

The woman is among 85 people who have been charged since the national terrorism threat level was raised on September 12, 2014, Victoria Police said.

There have been 36 counter terrorism-related operations nationally since the level was raised.

She did not apply for bail and is due to return to court on May 2.

The maximum penalty for the charge of engaging in a terror attack is live imprisonment.