The 36-year-old was involved in an altercation with goalkeeping coach Thierry Malaspina and both men had to be separated by other members of the first-team after Thursday's training session.
According to ESPN sources, tensions reached boiling point in the dressing room where the pair grabbed each other by the collar.
After the two men had been separated, Leca then punched a door in the dressing room and subsequently broke his finger to rule him out for the remainder of the campaign.
Sources have told ESPN that there has been tension between Leca and Malaspina for most of the campaign which resulted in Lens No. 2 goalkeeper Wuilker Farinez enjoying more playing time especially after the new year.
French newspaper L'Equipe initially reported the altercation and Lens released a statement on Thursday confirming the fallout between the two individuals.
"Following the publication of a report detailing an altercation, the club can confirm an excess of character shown by two members of the professional group at the end of training today," a club statement said on Thursday.
"Lens confirm that we will take the appropriate disciplinary measures and to clarify that the event which took place will be settled in the strictest privacy of the dressing room."
Lens are seventh in the league table and only two points adrift of a Conference League place. They face a trip to Troyes on Saturday before hosting Monaco in their final league match of the season next week.