Phogat, who has won three Commonwealth Games gold medals, was due to face Sarah Hildebrandt of the United States for the gold medal in Paris but was 100 grams (3.5 ounces) over the 50kg limit at the weigh-in for the final. She had made the weight before all her earlier bouts.
The Wrestling Federation of India (WFI) filed an appeal with global governing body United World Wrestling (UWW) to reconsider the decision.
Phogat asked CAS to award her a shared silver medal.
On Thursday, CAS said the matter which was examined by retired Australian judge Dr Annabelle Bennett as sole arbitrator, "has been dismissed".
"Consequently, the UWW decision is confirmed," the statement added.
Hildebrandt took gold in the final against Cuba's Yusneylis Guzman Lopez, who was reprieved after losing her semi-final to Phogat.
World bronze medallist Phogat, 29, was in the public eye for months last year as part of a long-running protest against the then-chief of Indian wrestling when he was embroiled in a sexual harassment scandal.
Following her disqualification from the Paris Olympics final, Phogat announced her retirement from wrestling.
