Palace was relegated to the Conference League, the third-tier European competition, by UEFA's Club Financial Control Body (CFCB) this month because John Textor, president of the Eagle Football Group, majority owners of Olympique Lyonnais, also holds a controlling interest in Palace.
Ligue 1 club Lyon, which also qualified for the second-tier continental competition, was permitted to compete.
"This (appeal) will undergo an expedited process with a decision (without justification) to be issued on or before 11 August 2025," CAS mentioned in a statement.
Last month, Palace announced that Robert Wood 'Woody' Johnson, co-owner of the New York Jets, had entered into a legally binding agreement to purchase Eagle Football Holding's share in the club, pending approval from the Premier League.
However, Palace did not meet the March deadline to adhere to the multi-club ownership regulations before winning the FA Cup in May, which secured their spot in European competition.
Nottingham Forest, who finished seventh in the Premier League, will take Palace's place in the Europa League if their appeal is unsuccessful.