Atal is also under investigation from French prosecutors and the French Football Federation for the post.
The 27-year-old, a member of Algeria's Africa Cup of Nations winning squad in 2019, has already apologised for the post in which a Palestine preacher wished harm Jewish people.
"OGC Nice understands that the player acknowledged his mistake by quickly removing the sharing of the publication and offered his written and public apologies," Nice said in a statement.
"Nevertheless, given the nature of the shared publication and its seriousness, the club took the decision to immediately take the first disciplinary sanctions against the player, prior to those that could be decided by the sports and judicial authorities.
"As such, the club has decided to suspend Youcef Atal until further notice."
"I am aware that my post shocked many people, which wasn't my intention, and I apologise," Atal, 27, said on Instagram on Sunday.
"I want to clarify my point of view without any ambiguity: I strongly denounce all forms of violence, wherever in the world, and I support all victims."
On Tuesday, Bundesliga side Mainz 05 suspended Anwar El Ghazi for publicly taking sides in the ongoing conflict.
