A search for a missing Melbourne kayaker has turned to be a false alarm.

An empty kayak was found washed up on shore on Thursday morning on a southeast Melbourne beach, about 100 metres from the Hampton Beach Lifesaving Club.

Police called for the owner to come forward and a Cheltenham man has since contacted officers.

The 39-year-old had ventured out in his kayak on Wednesday night but it started to take on water and began sinking.

He activated his life vest, left the kayak and swam to shore.