Mvila, 22, suffered the injury during Rennes' Ligue 1 victory over Paris Saint-Germain at the weekend.
Tests have confirmed a ligament problem although Rennes are unwilling to speculate on its severity just yet.
"Examinations revealed a sprained medial collateral ligament in his right knee," read a club statement.
"The duration of his absence is not known."
Mvila was recently suspended by the French national side until 2014 after visiting a nightclub prior to the second leg of an Under-21 play-off against Norway in October.
His lawyer has said the midfielder will appeal against the punishment.