It is understood he was one of a group of five swimmers who got into difficulty in the sea at Tullan Strand near Bundoran on Tuesday evening.
Four of the group were able to make it to safety with the help of local surfers.
Malin Head Coast Guard said the alarm was raised by a woman who was sitting in a car park as events unfolded.
Bundoran lifeboat and the coastguard helicopter, based in Sligo, went to the scene.
Shane Smith of Bundoran lifeboat said they believe the missing man is in his late 20s or early 30s.
"The conditions yesterday saw some quite heavy swell so they could have got into trouble because of that," said Mr Smith.
"We were on scene pretty quickly and a full search began. We also had members of the GardaÃ­ (Irish police) and defence forces helping as well.
"The search continued for a couple of hours but, of course, it is getting darker earlier now and we were stood down just after 21:00."
Tullan Strand is a popular surfing location and is regarded locally as a safe place to swim.
The search has resumed for a man missing off the coast of Donegal in the Republic of Ireland.