Mark Fosbrook, 28, from Cheltenham, has been training to compete with the British wheelchair rugby team in Athens.
The teacher said he was "devastated" when the ruling body for the sport told him he was too able-bodied to play in the Paralympics, which start on September 17.
Mr Fosbrook, who competed with the British Paralympic volleyball team in Atlanta in 1996, said he felt "frustrated and annoyed".
He said: "I am annoyed because I am sure I am eligible. I was born with no feet and just two fingers on each hand.
"I have been training with the squad and now I am going to miss out. I am absolutely gutted."
The International Wheelchair Rugby Federation rejected Mr Fosbrook's appeal against their classification decision.
They ruled that his hands scored three points - four being the level classified as able-bodied.
His body also scored a point as he has full use of his abdominal muscles.
This means Mr Fosbrook has four points which is too many to compete at a national level.
A spokeswoman for the International Paralympic Committee said wheelchair rugby players must qualify for one of seven groups from 0.5 to 3.5 depending on their functional ability.
I'm not sure what this is a better example of: of how attempts to define phenomena often lose sight of that which they are supposed to be defining, or, yet again, of the unintentional but inevitable malice of bureacracy.