Reports in France indicate that Gueye opted out of the game as he was against Ligue 1's support for the LGBTQ+ community.
Ligue 1 games over the weekend featured all teams wearing rainbow-coloured numbers to mark the 2022 International Day against Homophobia.
Gueye was missing from the PSG squad which was attributed to 'personal reasons' by manager Mauricio Pochettino.
Gueye has received support from some members of the Senegal national team for his actions as well as his country's president Macky Sall.
But Gueye's no-show constitutes discriminatory behavior according to the French FA, who have asked him to explain the reason behind his absence.
"This absence (against Montpellier)... is very widely interpreted as a refusal to participate," the French Football Federation's (FFF) ethics board said in a statement seen by APF.
"One of two things, either the hypotheses are unfounded and we invite you to immediately express yourself in order to silence these rumours.
"Or the rumours are true. In this case we ask you to be aware of the impact of your actions and the very serious error committed.
"In refusing to take part in this collective initiative you are validating discriminatory behaviour... and not only against the LGBTQI+ community."
Gueye has made 32 appearances across all competitions for PSG this season, scoring four goals.
