Sakho allegedly grabbed Der Zakarian and threw him to the floor when he was not awarded a foul during a training ground exercise.
The 33-year-old denies the allegations.
Sakho joined Montpellier as a free agent in the summer of 2021 after leaving Crystal Palace and has made 49 appearances.
Only six of those appearances have come under Der Zakarian, who joined Montpellier in February.
A statement released by Sakho on Instagram read: "You have to know how to leave the table when respect is no longer served.
"Following the incident that took place last week at the training centre and for which I decline all responsibility, I have decided on this day of 02/11/2023 to end my collaboration with Montpellier Herault Sports Club.
"I spent two years in this family club where I took pleasure to share my high-level experience with my teammates and my “little brothers” from the centre of training.
"At the same time, I thank them for their support as well as the medical staff without forgetting the supporters who appreciated my time at the club."
"Thanks also to the sports director Bruno Carotti for his loyalty to me throughout my Montpellier adventure."
"Finally, I wanted to give a special thanks to the president, Laurent Nicollin, who like his late father did before him, heads the MHSC with the values and principles that are dear to me."
"We met as men, we leave as men. Happy end of the season."
Sakho counts Paris Saint Germain and Liverpool among his former clubs and has played 29 times for the France national team.
