The last sighting of the man was when a member of the public saw him going from his yacht into his inflatable tender off Kinloch on the Isle of Rum at around midnight on Tuesday, the coastguard said.
The member of the public raised the alarm at around 10pm on Thursday night when they realised the man had not moved his yacht to another location as expected.
Extensive searches have been carried out but nobody has been found on the yacht and no trace has yet been found of the man or tender.
A coastguard spokeswoman said they are carrying out an “extensive search” around the Isle of Rum, south of Skye and the other Small Isles.
Mallaig RNLI lifeboat, Tobermory RNLI lifeboat and Mallaig Coastguard Rescue team are involved in the search, while a coastguard helicopter helped on Thursday night.