The Romanian club's board made the decision following a run of results that has seen the team collect just 16 points from 12 matches in their domestic league.
"CFR Cluj's club management and Ioan Andone have reached an agreement to end relations," the club said in a statement.
"We are proud of everything we've accomplished together. Andone has and will always have a special place in the hearts of our supporters."
Andone's last game in charge was yesterday's 1-1 draw against Galatasaray.