The north-east club believe the decision taken by Senegal to prevent Cisse from playing on Saturday is a direct retaliation to them withdrawing the striker - because of injury - from the country's midweek international friendly against Niger.
Newcastle say they followed the necessary rules in accordance with FIFA only for the Senegalese Federation to deny Cisse the chance to play for his club a few days later.
A statement on the club website reads: "Newcastle is dismayed and angry at the position adopted by the Senegalese Federation, and supported by FIFA, which means that Papiss Cisse is unable to play any part against Swansea City.
"Immediately following the fixture against West Ham United on Sunday the club went through the normal communication channels to advise the Senegalese Federation that Papiss would not be available for the international friendly due to injury.
"No reply was received and as such further communications were sent to the federation on Monday, 12th November.
"The club was not prepared to allow Papiss to travel to Niger as this would have been detrimental to his clinical condition.
"In accordance with FIFA Regulations the Club was more than happy for the player to be examined in England by a doctor of the Federation's choice in order to validate the player's medical condition.
"The Federation did not take this option and instead contacted FIFA to ask them to apply the regulation that effectively prevents Papiss from playing this weekend.
"It is the opinion of the club that it is wrong and wholly unjust for a national association to behave in this manner and for FIFA to endorse their stance and automatically apply the sanction without taking into account the specific facts of the case.
"The club understands that a number of other players were withdrawn from the Senegal squad. To the best of our knowledge Papiss Cisse and Newcastle United are the only parties that the national association has sought sanctions against."
Newcastle went on to say that the Senegalese Federation "have an agenda against Papiss and/or Newcastle United, possibly as a reaction to the club's decision earlier this year not to allow Papiss to participate in the London Olympics."
The St James Park club added they "will be speaking to its legal advisors to see if it has recourse against the Senegalese Federation and/or FIFA."
Cisse admitted he was now considering his international future after being left bemused by the chain of events.
He said: "I am deeply disappointed by the actions of my Federation which have punished me and my club.
"I love playing for my country and would only withdraw from a squad - for either a friendly or competitive game - for a genuine reason.
"I am fully supportive of the position my club has adopted in this matter and am sorry that the Federation seem to doubt my honesty and integrity.
"I will now consider if I wish to continue to captain my country."