The body of a man who went missing while fishing off Queensland's Sunshine Coast has been found not far from where he disappeared.

Luke Howard, 35, was fishing with a friend on a jet ski in calm waters near Mudjimba Island when he went missing.

He had taken his life jacket off and entered the water to investigate problems with his jet ski, which was taking on water.

Police said Mr Howard was unable to climb back on.

He clung to the back of the jet ski as his friend tried to drive them back to shore, but disappeared from sight.

Mr Howard has been described as a fit person who regularly swam from Coolum to Mooloolaba and competed in triathlons.