US media reported that Mr Gilbert had been involved in a domestic argument.
No-one has been arrested. Police want to speak to Mr Gilbert?s son in connection with the incident.
US media said the body was found at about 15:30 local time (20:30 GMT) in a bedroom in the flat in Beekman Place, and that a gun had been recovered from the room.
?Right now, we?re looking to speak to his son, who was the last person to see him alive,? police spokesman Lt John Grimpel said, without identifying the son.
Mr Gilbert was a graduate of Princeton University and Harvard Business School.
The hedge fund focuses on the biotech and health care industries.