Volatile keeper Joudren went on the warpath after the defending French champions lost 3-2 to Evian in Ligue 1, which followed a 2-2 Champions League defeat to Schalke.
Girard said that he had summoned Joudren for talks and that he will take action accordingly.
“Things have happened that I cannot tolerate,” Girard said. “We have had a meeting and we discussed everything man to man. I will do what I have to.”
Joudren had questioned the decision to replace Hilton and Remy Cabella with Daniel Congre and Emmanuel Herrera.
“Why change a winning team?” he told a local radio station. “Why would you do that? We need to ask the right questions and if it hurts, it hurts.”
Congre had been brought in ahead of Hilton following the LFP’s decision to ban Mapou Yanga-Mbiwa for five matches after he elbowed St-Etienne’s Romain Hamouma.
If Joudren is dropped, Laurent Pionnier would make his first Ligue 1 start for over a year.
Montpellier, surprise champions last season, have struggled this campaign as they juggle domestic and European commitments following the sale of top scorer Olivier Giroud to Arsenal.