In Greek mythology, Apemosyne was a daughter of Catreus and sister of Althaemenes.

An oracle told Althaemenes that he would murder his own father. Althaemenes took Apemosyne and left Crete for Rhodes. A despondent Catreus sailed the seas searching for his children. In the middle of the night, his ship stopped at Rhodes and was mistaken for a pirate ship. Althaemenes and others attacked the ship, and the prophecy came to pass; Catreus died at the hands of his son.