Officers said they had alerted the family of 26-year-old Nitin Woocheet, from Southsea, who has been missing from Portsmouth since 18 March.
The body, which has not yet been identified, was discovered by crew on a fishing vessel on Sunday evening.
It was then recovered by the RNLI's Bembridge Lifeboat.
A spokesman for Hampshire Constabulary said: "Officers are in the early stages of an investigation into the death, which at this stage is unexplained."
A man's body has been pulled from the English Channel off the Isle of Wight after an "unexplained" death, police have said.