FIFPro called on soccer's governing body FIFA and the Qatari FA to end the impasse, saying they were capable of doing so "immediately".
"We are of the view, and the FIFA regulations are clear, that if a player has a dispute with his club, he should be able to continue to play while the dispute is resolved," Brendan Schwab, head of FIFPro's Asia division, told Reuters on Friday.
"In this case, not only can the player not continue his career, he cannot even move."
Belounis, who went to Qatar on a five-year contract with Al Jaish club, has been prevented from leaving since February after he filed a lawsuit for 18 months' worth of unpaid wages, according to local newspaper the Doha News.
"He has no freedom of movement as a human being, as a citizen, and so we think it's not only a violation of the footballer's rights but it's a fundamental violation of his rights as a human being," Schwab said.
"We think it's time to stop and say the football family cannot be united if the human rights of the players are not being respected."
Belounis is unable to leave Qatar, which will host the 2022 World Cup, without an exit visa which his employer has to obtain for him.
Although there were reports a week ago that Belounis was about to receive his exit visa, FIFPro said they understood he was still in the country.
Several reports on Twitter also said he had yet to be allowed home.
"I'm optimistic about the success of the football dialogue we have with the authorities in Western Asia, but we do need them to understand that situations such as the one with Belounis are not acceptable," said Schwab.
"FIFA and the Qatari FA could stop this problem with Belounis immediately and we call on them to do so... by instructing the club to issue the necessary exit visa."
He added: "FIFA is loathe to do so (intervene)."
Schwab said that, elsewhere, there had been a "huge effort" to help Belounis.
"The international trade union movement has been involved, letters have gone to the French government, letters to the French president and I think that goes to show just how difficult it can be to get a simple outcome like that.
"Belounis was contemplating a drastic action (hunger strike) in order to be released and it's a tragic set of circumstances, where players have to resort to that to have their rights respected.
"If Eastern Europe and Western Asia... are going to be rewarded with the great events and great honours of hosting the World Cups, we think it's very important that universal human rights standards apply, and more modestly that the standards agreed between FIFA and FIFPro apply in every country in which professional football is played."
Earlier this year, former Morocco international Abdeslam Ouaddou said he was the victim of a similar situation in Qatar, telling FIFPro's website he had been "treated like a slave" in a dispute with a top club.
"We highlight these problems but the opportunities on offer financially in Western Asia, including Qatar and the United Arab Emirates, can be as attractive as anywhere in the football world," said Schwab.
"There are some very substantial contracts on offer but players need to be aware when they go that there are certain aspects that are unique and we are learning about these all the time."
Schwab said that, at 33, Belounis was unlikely to play professionally again, even after he got out.
"This will end the player's career in all likelihood because the career is short term and precarious and it's very difficult for a player to miss a substantial period of his career and then continue."