Stornoway Coastguard received a mayday call at 23:41 on Friday alerting them to the boat in distress.
The yacht had two adults and four children on board and the occupiers feared it was sinking.
Coastguard teams launched an air and sea mission to get to the aid of the boat, which was stranded near Calve Island, south east of Tobermory Bay.
The Oban lifeboat and the Rescue 951 helicopter from Inverness were sent to the scene, a coastguard spokesman said.
The lifeboat was first on the scene and managed to rescue everyone on board.
The helicopter stood by and provided lighting in the area.
"There were no injuries and everyone was taken off safely," the coastguard spokesman said.
The boat was floated off at high tide on Saturday.
Six people have been rescued from a yacht after it ran aground in the Sound of Mull.