Rougier and Manchester United's Dwight Yorke failed to travel with the rest of their international team-mates for a warm-up friendly against Panama last weekend.
And the Trinidad and Tobago Football Federation (TT&FF) have taken the tough decision to drop the duo despite the knowledge that defeat will all but end their chance of qualifying for next summer's World Cup finals in Japan and South Korea.
Shaun Fuentes, press officer for the TT&FF, told the Evening Post: "A management committee came to the decision on Tuesday that Tony and Dwight will not be able to play on Saturday.
"Tony was in Trinidad and Tobago last Thursday when the team flew out to Panama but he did not travel with the team.
"And the committee, made up of technical staff, felt that all players should have travelled as it is a critical period for the team."
Rougier and Yorke will be considered for Trinidad's World Cup qualifier with USA next Wednesday. A decision will be made after a meeting between TT & FF president Oliver Camps, technical director Rene Simoes, coach and former Royals boss Ian Porterfield, manager Neville Chance and the rest of the players.
Rougier, a £340,000 signing from Port Vale, is known to be carrying an ankle injury sustained while playing for Reading earlier in the season.
The Evening Post exclusively revealed that he will need an operation in the summer and he has been booked in to London's Brompton hospital on July 3 to have fragments of bone knocked off the injured ankle.
However, the TT&FF have decided that even if Rougier did not want to aggravate the injury in a friendly match, he should still have travelled with the rest of the team.
Yorke, on the other hand, missed the friendly because he was out nightclubbing.