The 27-year-old was unavailable to manager Alan Pardew after the Senegal Football Federation, with the support of FIFA, invoked the governing body's five-day rule following his failure to report for international duty in midweek because of a back injury.
Newcastle released a statement which said they were "dismayed and angry" at the situation and voiced the opinion that they may be being punished for refusing to allow Cisse to represent his country at the Olympic Games earlier this year.
The player also expressed his disappointment and revealed the decision could have wider implications.
Cisse 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."
Cisse was withdraw from the Senegal squad for their friendly against Niger after limping out of last Sunday's 1-0 Barclays Premier League defeat by West ham with a back problem.
Newcastle claim they sent details of the injury to the federation's medical department, but heard nothing back until it emerged that they were seeking to stop him playing on Saturday, and are now seeking legal advice on the matter.
The statement said: "Newcastle United 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 in Saturday's Premier League fixture against Swansea City.
"Immediately following the Premier League fixture against West Ham United on Sunday, the club went through the normal communication channels to advise the Senegalese Federation that both Papiss and Demba Ba would not be available for the international friendly match between Niger and Senegal scheduled for Wednesday, 14 November 2012 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 is disappointed, although not in any way surprised, that FIFA has disregarded its submissions and valid points in relation to this matter and instead have supported a national association which ignored repeated attempts by the club to engage with them and, furthermore, insisted on a course of action which would have had a detrimental impact on the player's physical condition.
"The club understands that in addition to Papiss Cisse and Demba Ba, 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.
"It is the club's genuinely-held view 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 2012.
"The club intends to take this matter up with the Football Association and any other relevant body within the game to try to stop national associations/federations and FIFA from preventing an employee (a player) from fulfilling their contractual obligations to their employer (a club).
"The club acknowledges the importance of international football and the great honour players undoubtedly get from representing their country.
"That said, national associations and FIFA should have a duty of care to clubs with regards to their players and it cannot be allowed to continue that national associations can, as in this case, seek to act in a way which is not in the best interests of a player and compromises their well-being and, furthermore, is then able to apply to FIFA who impose a sanction which damages that individual and his employer without a fair and equitable process being applied.
"The club will be speaking to its legal advisors to see if it has recourse against the Senegalese Federation and/or FIFA."