A man has been arrested and is in hospital under police guard after a woman was found stabbed to death at a suburban home.

Police were called to a property on Delatite Court, a leafy residential street in Melbourne's outer-eastern suburb of Vermont, just before 10pm on Tuesday. 

It followed reports a woman had been stabbed inside a home.

When officers arrived, a 39-year-old woman was found dead at the scene. 

A man of the same age was arrested and treated by ambulance paramedics before being taken to hospital under police guard. 

Police believe the man and woman know each other.

"The investigation into the circumstances of the incident is ongoing," Victoria Police said in a statement.

The man would be interviewed by detectives and the homicide squad had taken carriage of the investigation.