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.

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 Roger, 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 the 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.

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

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

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

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

Ms Shoma made no application for bail and was remanded in custody.

Police are executing search warrants at the home in Mill Park and at another home in Bundoora, where the woman had previously stayed.

However, police said there was no suggestion the residents of the Bundoora home were involved in any way.

The woman had been enrolling in a course at La Trobe University and police said it is understood she was wearing a black burqa at the time of the incident.

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

“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.”

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

“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.

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.