The five-time world champion and Olympic silver medallist in London broke his radius after falling off his bicycle in a training accident in Lugo, reports Xinhua.
X-rays confirmed the injury, which will need an operation that leaves him with no time to recover for Rio.
"It is hard to understand how all of that effort and those hopes that I had put in the Olympic Games can suddenly disappear, but I have no option other than to accept it and to start thinking about making a good and rapid recovery," Gomez Noya said in the Spanish press on Friday.
His absence means that the UK's Brownlee brothers, Alistair and Jonny, who won the gold and bronze medals on home soil four years ago, will again be the favourites in Rio.
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