North Yorkshire Police were called to The Beacon in Marne Road, Catterick Garrison, at around 11.30pm on Friday following the discovery of a 34-year-old with fatal injuries.
It was believed he had been stabbed.
A North Yorkshire Police spokeswoman said: "Police are investigating the full circumstances surrounding the death and officers continue to work at the scene.
"The arrested man remains in police custody whilst inquiries continue.
"We are not in a position to identify the man who died."
Anyone with information is asked to call 101.
According to its website, the Beacon offers supported housing to single veterans "who are homeless or at risk of homelessness and who have support needs".