Earlier on Wednesday, German side Mainz suspended Dutch international Anwar El Ghazi for what it called an "unacceptable" social media post about the conflict in the Middle East.
Atal's suspension comes after the Nice public prosecutor's office opened a preliminary investigation on Monday, targeting him on charges "of defending terrorism" for sharing the message online.
The 27-year-old is also being investigated for "public incitement to hatred or violence because of a particular religion", the office said.
Nice said it had discussed the issue with Atal, who has since apologised and deleted the Instagram post.
In a statement, Nice said: "The player acknowledged his error by quickly withdrawing the sharing of the publication and has offered a written and public apology.
"Nevertheless, given the nature of the publication shared, and its seriousness, the club has made the decision to immediately take the first disciplinary measures against the player, prior to any action that may be taken by sporting and legal authorities.
"To this end, the club has decided to suspend Youcef Atal until further notice."
French Football Federation (FFF) President Philippe Diallo said Atal had relayed "appeals for violence" and that the case will be handled by the federation's ethics committee.
El Ghazi, meanwhile, has been relieved of his "training and matchday related duties", Mainz said in a statement.
"In the post, El Ghazi stated an opinion on the ongoing conflict in the Middle East that was deemed unacceptable by the club," a statement read.
"Prior to making this decision, the club and the player had engaged in an in-depth discussion."
The Bundesliga club did not specify what the social media post contained, nor whether the 28-year-old forward will return to play for the club.
El Ghazi has previously played for Premier League sides Aston Villa and Everton, and has been capped twice for his country.
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