Scottish champions looking into Tweets he sent out on Sunday ahead of Inverness game.
The Irish international tweeted about his his frustration at being left out of the matchday squad ahead of their win at Inverness Caledonian Thistle on Sunday.
Stokes soon apologised to the club and fans, but now Celtic have opted to suspend Stokes - who is understood to be mystified at the club's stance.
Celtic have suffered from a number of off-field issues in the past 12-months, from captain Scott Brown being pictured slumped in the street to more recently Kris Commons launching a verbal tirade at boss Ronny Deila after he was substituted during their Europa League loss to Molde.
However, whilst Brown and Commons both avoided any internal punishment from the club and Deila, Stokes has not. Many Celtic fans are bound to be shocked by the stance, given Commons - especially - was not reprimanded for his public verbal assault on the coach.
A spokesman for the player confirmed: "We can't comment on the situation, but the club did inform Anthony on Tuesday that he would be suspended."
Stokes, who has scored 59 goals in 107 league starts for the Bhoys, has barely featured under Deila this term - despite the club's struggles, especially in Europe.