The IGF wanted Cas to compel the International Gymnastics Federation (FIG) to “take the necessary measures that guarantee Israeli participation in the championships” or “to move or to cancel” the event, which runs until 25 October.
It said the FIG’s lack of measures was a “denial of justice” and created a “situation of discrimination against a member association”.
A Cas statement said the FIG argued it had “no prerogatives” in the issuing of entry visas, and the Indonesian government’s decision not to grant the visas falls “outside the competence” of the organisation.
An IGF statement read: “The rules are clear, and Indonesia’s actions constitute a blatant violation of them.
“It is inconceivable that a country can bar another nation from competing in a World Championship while the governing bodies stand by.
“This decision undermines the very foundations of sport and fair competition, and it delivers a severe blow to the morale of the gymnasts and staff who have worked tirelessly for this moment.”
Dolgopyat said on Instagram: “We are so disappointed for the gymnasts, male and female, and professional teams, but not only that, we are deeply concerned by the recent decisions that could negatively impact the future of all our delegations and the future of sport in general.
“We continue the fight, hoping to achieve justice, but unfortunately we will no longer be able to compete in these World Championships.”
Dolgopyat was one of six gymnasts – alongside Eyal Indig, Ron Pyatov, Lihie Raz, Yali Shoshani and Roni Shamay – who submitted the requests to Cas in conjunction with the IGF.
Dolgopyat, 28, won Olympic floor gold at the Tokyo 2020 Olympics and silver in Paris last year. He is also a two-time European champion.
On Monday 20 living Israeli hostages and hundreds of Palestinian detainees were reunited with their families as part of a ceasefire deal.