A Carnival Cruise ship made a U-turn to search for a man who jumped overboard into the waters off Mexico … and one of the passengers taking the trip told TMZ all about the tragic event.

The search began on Saturday morning as the ship was heading along the coast of Mexico’s Baja peninsula.

A rep for Carnival tells TMZ … “Carnival Cruise Line confirmed Saturday that a male guest aboard Carnival Panorama jumped overboard while the ship was sailing from Puerto Vallarta, Mexico to Long Beach, California.”

When they were notified that a guest was missing, the crew reviewed CCTV footage as part of their investigation and alerted both the U.S. and Mexico Coast Guards.

The cruise line added … “Carnival is providing support to the family who was traveling with the guest, and our thoughts and prayers are with them and their loved ones.”

A passenger tells TMZ … the incident occurred in the waters along the Baja peninsula as the ship was returning to Long Beach.

The cruise ship guest added … a family member had guest services page the missing passenger around 10:30 AM after searching for him.

After CCTV footage confirmed he went overboard, the ship turned back around at 2 PM to search before resuming its route to Long Beach at approximately 4:30 PM … the passenger says.