The LFP's disciplinary committee announced the preliminary measure on Monday following a series of incidents during a derby clash with Nimes a day earlier.
With the rivals playing for the first time in 25 years, the game was marred by a long second-half stoppage.
When Gaetan Laborde put the hosts 3-0 up, supporters of each club faced off in the stands, leading to riot police using tear gas to disperse fans.
Referee Ruddy Buquet stopped the match for a period of around 20 minutes, the match resuming after order had been restored by police.
"Given the seriousness of the matter, the disciplinary commission has decided to open an investigation into the matter and provisionally close the away sector for Montpellier fans travelling to games, to close the lower section of the Etang de Thau Stand and the upper section of the Petite Camargue Stand," read an LFP statement released.
Ambroise Oyongo's opening goal in the first half led to a barrier collapsing in one of the Montpellier stands.
Andy Delort also scored for Montpellier in a comfortable win that leaves them third in Ligue 1 after eight games.