Musa joined Fatih Karamguruk in July 2021 after leaving Nigeria Professional Football League's Kano Pillars.
The club announced the termination on their Twitter handle without stating any reason for the decision.
The 29-year-old made 34 appearances for Fatih Karamguruk without scoring.
He has made two appearances this season against Alayanspor and Besiktas in the Turkish League.
Ahmed Musa has been strongly linked with a move to Sivasspor.