In a statement, posted on social media, the Royal Bahamas Police Force said: "According to the preliminary report, shortly after 10am, officers at the Alice Town police station received information that a female was unresponsive at the North Bimini Ferry Dock.
"Officers responded and, upon arrival, learned that the woman had been transported to the local clinic for medical attention, where she was subsequently pronounced dead by a local doctor despite efforts to save her life.
"Preliminary information indicates that the deceased was snorkelling with her husband and two sons near the southern point of the island when a strong current reportedly swept both children away.
"In an attempt to rescue her sons, the woman was also swept away.
"She was later rescued and transported to the ferry dock, where CPR was reportedly administered.
"Foul play is not suspected at this time.
"An autopsy will be conducted to assist in determining the exact cause of death."
A spokesperson for the Foreign Office said: "Our thoughts are with the family of a British woman who has died in the Bahamas.
"We are in contact with the local authorities and providing support to her family."