Both were punished for tirades aimed at referees which were shown by Canal Plus. As a reprisal, PSG and Marseille say they will not answer the station's questions after games or at press conferences until the end of the season.
Paris coach Laurent Blanc rejected a question from Canal Plus after Saturday's League Cup final win over Bastia. The channel attended Blanc's press conference Tuesday ahead of PSG's Champions League quarter final clash against Barcelona, but it did not try to ask a question.
Paris are furious at a four-match ban imposed after Canal Plus pictures showed Swedish star Ibrahimovic in an expletive-laden rant against referees and France after his side lost at Bordeaux.
French international Payet was banned for two matches for shouting at the referees room that Marseille had been "screwed" after a goal was disallowed in their 0-0 draw with title rivals Lyon. Again it was shown by the subscription broadcaster which, with BeIn Sport, has the rights to show French league games.
France's two most popular clubs said in a statement they "do not want to take the risk of being open to new sanctions linked to unfortunate comments provoked by a controversial refereeing decision."
They added that "the number of Canal Plus group cameras and microphones that surround the teams in all circumstances, and the possibility of a retroactive judgement after the showing of images used as proof by football judges lead us to adopt this very great caution."
Canal Plus deputy director general Maxime Saada told AFP that the channel had become a "hostage" between the clubs and league disciplinary judges because of film taken around the Ligue 1 matches.
He said this was "stopping our teams of journalists from carrying out their jobs."
Saada said that Canal Plus was a "respectful partner" of French clubs and wants only to show "the spectacle of Ligue 1 and its 20 clubs in its totality."
The channel currently pays 420 million euros ($448 million) a year to show French matches and from 2016 this will rise to 540 million euros a year.
Despite Canal Plus protests, French clubs have been showing increasing mistrust of the channel.
According to media reports, the Professional Football League planned to send Canal Plus an official letter warning it to stick to their contract.
Under the deal between the broadcaster and the clubs, it promises "not to promote scenes contrary to the image of football" and "to give a positive image of football putting the emphasis on beautiful gestures and the beautiful game."
League officials have indicated that if Canal Plus does not change its ways it could be stopped from filming off the pitch.
Some clubs also feel they get a more critical treatment from Canal Plus than from the rival BeIn Sport, representatives told AFP.
But Lyon coach Hubert Fournier said television channels should not be "falsely accused" for the actions of players.
"From the moment you accept them (TV cameras) in these mixed zones, it is for the actors to be conscious of their comments and actions to avoid this kind of scandal," said Fournier.
The French government's Secretary of State for Sport Thierry Braillard said he was "profoundly surprised and disappointed" at the decision of Paris and Marseille.