A passenger has died after going overboard from a Carnival cruise ship near the Bahamas ... TMZ has learned.

Sources on board the boat tell TMZ ... the man went into the water from the Carnival Liberty as it traveled just outside Nassau Tuesday. We're told a life ring was thrown to him, but he was soon out of sight, prompting an immediate search and rescue effort.

A Carnival spokesperson tells TMZ ... the guest climbed over his stateroom balcony and went overboard while the ship was sailing from Celebration Key to Nassau. Crew members immediately launched a search and were able to recover him from the water, but he did not survive.

The cruise line says it is now supporting the guest's family, who were traveling with him.