“I tendered my resignation for personal reasons,” he told the AA, describing his decision as "final".
“The political division in the street has stymied my effort to promote the Egyptian sports,” he said.
A source with the Sport Ministry confirmed that Amry has faxed his resignation to Qandil.
The ministers of foreign affairs, environment, communications, tourism and legal and parliamentary affairs have earlier tendered their resignations.
At least two governors and 24 lawmakers have also quit.
Hundreds of thousands of protestors have been staging protests across Egypt to call for President Mohamed Morsi’s resignation and demand snap presidential elections.
But supporters insist the Islamist president, who was elected in June 2012, must complete his four-year term.
The army has given all parties a 48-hour ultimatum to find a solution to the crisis before intervening.
But the presidency hit back, saying President Morsi was not consulted about the army ultimatum and that "the mechanism of democracy are the only way to solve the crisis."