The 29-year-old, who made his professional debut back in the 2005/06 season, joined the club from Bidvest Wits after many years at Golden Arrows.
He has played over 50 games for Celtic – 15 this season – and parts the club on good terms.
“Musa asked for his clearance and because of his professional conduct in dealing with the matter we agreed,” club managing director Rali Ramabodu says.
“He served the team with absolute distinction and we wish him all of the best with his future endeavours.”
Celtic earlier released left-back Tumelo Mogapi, while striker Hellings Mhango has joined Wits.