The victim died around 8.30pm on Saturday (3 May) following an altercation on the 6,334-passenger ship.
Hampshire and Isle of Wight Constabulary confirmed his next of kin have been informed and are being supported by specialist officers.
A 57-year-old man from Exeter has been arrested on suspicion of murder. A police spokesperson confirmed the man is still in custody.
Virtuosa was two and a half hours into a two-day sailing to Bruges when the altercation occurred.
Detective chief inspector Matt Gillooly, from Hampshire and Isle of Wight Constabulary, said: "We want to reassure you that this appears to be an isolated incident on board, and we want to thank the crew for their cooperation and assistance with our inquiries.
"If anyone who was onboard has information that could assist, please contact Hampshire and Isle of Wight Constabulary on 101 with reference 44250193676.”
A MSC Cruises spokesperson said: "Following an incident on board our ship, the relevant authorities were contacted, and we are cooperating fully with their investigations. We are providing full support to those impacted and thoughts are with the family and friends at this difficult time."