The 43-year-old victim died in hospital on Friday after sustaining injuries at West Melbourne's Flagstaff crisis accommodation centre around 7.30am.

A 44-year-old man was charged with one count of murder on Friday afternoon and was due to face Melbourne Magistrates' Court.

The Salvation Army said it was providing assistance for staff and residents.

"Residents and staff are obviously shaken by this unexpected incident and the Salvation Army is providing counselling to support them during this period," the organisation said in a statement.

The Flagstaff centre is a state-wide crisis service providing accommodation, meals and welfare support for 64 men.