The south coast club has dominated French handball for the last 15 years and officials were quick to protest the innocence of their players, many of whom starred for the France team that won Olympic gold in the London Games.
A legal source confirmed that some players and their relatives would soon be questioned as part of the probe.
Montpellier president Remy Levy, a lawyer by profession, told the Midi Libre newspaper that he and coach Patrice Canayer had already been quizzed by police heading the investigation, without giving further details.
"I will defend the honour of the club," Levy said, adding that all club players knew the rules banning sporting bets.
"The cited players do have the presumption of innocence. We'll see what the investigation establishes. We'll see the truth behind these claims, these
bets, the identity of people who will be interviewed."
Suspicions were raised over a match that Montpellier lost 31-28 to Cesson-Sevigne on May 12. At the time, Montpellier were assured of a 13th league title in 15 seasons while the Breton club sat in eighth position.
Betting firm la Francaise des Jeux (FDJ) at the time reported abnormal betting patterns up to five times bigger than expected and suspended bets during the match.
Large bets reportedly came in at half-time on a loss for Montpellier, for whom stalwarts Nikola and Luka Karabatic, Mladen Bojinovic, Vid Kavticnik and Samuel Honrubia were not playing because of injury.
France 3 television reported that police had discovered that wives or girlfriends of players and club members had placed bets in three betting shops in the Paris region, the western region of Brittany, and around Montpellier.
Montpellier are currently in Germany where they are preparing for a Champions League match against Flensburg on Thursday, before returning to the French capital to play Paris Saint-Germain in a top-of-the-table league clash on Saturday.
"What should have been a big handball festival has been tarnished," said Montpellier president Levy.
"It's obviously the image of the club brand that's at stake. We've got a good image. We'll fight to restore our honour."
Cesson president Philippe Barberet said he was baffled by the investigation.
"No one saw anything during the match," he told RTL radio. "I don't understand. If ever these players were really involved in anything, it would really be a tragedy."