The former France international was appointed in January, following a disappointing six-month spell in charge of Bastia in 2014.
Monaco - who finished third in Ligue 1 in 2015-16, earning a place in the play-offs for next season's Champions League - announced Makelele's departure on Monday.
"AS Monaco and Claude Makelele announced today the completion of their co-operation by mutual agreement," a statement read.
"The club would like to thank the former French international for the work undertaken since his arrival. AS Monaco can only wish the best for Claude in his future endeavors."
"I thank the club and [vice president] Vadim Vasilyev for the confidence they placed in me by offering me the chance to join AS Monaco," Makelele said. "Our destinies are separated but I wish AS Monaco the best for the future."
"Claude is a professional and a man of great level. He brought his experience, particularly on structure of the academy," added Vasilyev.
"I'm sure he has a lot to give in football and he will always be welcome in Monaco. Neither the club nor he managed to find the ideal position within the sports structure. He was honest enough to open up to me about this and we decided together to end the collaboration on good terms. "