Bin Hussein alleged that FIFA verbally communicated during the World Cup that endorsing Infantino "would go a long way to helping our FA out" after months of the world soccer governing body refusing assistance on various matters.
"We pride ourselves in Jordan in upholding ethical values. We did not endorse him before and certainly will not now," Bin Hussein wrote on X.
"But the whole situation amounts to blackmail and we refuse to give in to that."
Reuters has contacted FIFA for comment on all allegations.
His rebuke comes as Infantino faces growing opposition within soccer's hierarchy after the FIFA president was forced to abandon a controversial proposal to sell off a stake in the World Cup.
Soccer confederations and national associations rejected the idea following a hard September 19 deadline imposed by the Swiss official.
FIFA had argued that selling the minority stake in its commercial operations would raise billions of dollars to fund global sports development.
FIFA Secretary General Mattias Grafstrom and Arsene Wenger were among executives who distanced themselves from Infantino, with Bin Hussein saying there was a problem with the leadership.
The Jordan FA chief outlined a number of grievances facing his association as a small nation with a "minimal budget."
These included fans paying "exorbitant prices for tickets" while still being denied visas for the World Cup in the United States and outstanding reward money for players' participation in the 2025 Arab Cup, a FIFA-organised tournament.
Adding to Jordan's woes, Bin Hussein complained about being taxed by the U.S. government through FIFA for World Cup participation - costs not faced by teams based in Canada and Mexico.
"We are being taxed by the U.S. government through FIFA for our participation. Money that should go to players and staff," he added.
"This was not the case for those who played and set up camp in Canada and Mexico. But we happened to be in the USA so now we face these huge costs in taxes for having participated."
Jordan qualified for the World Cup for the first time but exited in the group stage.
The association has also been waiting since December for reward money for reaching the Arab Cup final in Qatar.
"The money our team should receive for having reached the final has not been delivered yet, while at the same time FIFA brags about how many billions they have in reserve," Bin Hussein added.