Royal Grenada Police Force said the body of David John Foster, 76, was discovered on Paradise Beach in the village of L’Esterre, Carriacou.
Rosaline Foster, 77, was found on the same beach and taken to the island’s Princess Royal Hospital where she was pronounced dead, officers added.
Police attended the scene and are investigating Saturday’s incident.
A post-mortem examination will be conducted to determine a cause of death.
Paradise Beach was voted the best Caribbean beach of 2022 and is known for its “crystal clear calm waters”, according to the Grenada Tourism Authority.
The 13-square-mile island of Carriacou is the second-largest in Grenada and a 20-minute flight from the main island, it added.