The 31-year-old missed the 3-1 win over Hibs at Parkhead on Saturday after Hoops manager Ange Postecoglou revealed the midfielder was feeling "sore" after playing through muscle pain in recent weeks.
Mooy has emerged as a key first-team figure at Celtic since returning from the World Cup in Qatar, where he started every match as Australia reached the knock-out stages for the first time in their history.
However, the Socceroos will have to make do without their influential talisman for the upcoming friendly double-header against Ecuador after Mooy opted to remain in Scotland to focus on his recovery. The decision was taken following consultation with medical staff at both Celtic and the Australia national team.
St Mirren's Ryan Strain has been called up in his place with the Buddies right-back handed a chance to stake a claim after making his international debut against New Zealand in September last year.
Commenting on Mooy's absence, Australia boss Graham Arnold stressed that the injury is not serios.
He said: “It’s unfortunate for Aaron that he misses these games, something I know he was very much looking forward to playing, but his absence provides an opportunity to a further emerging player as we start this new campaign.
“After speaking with Aaron, who missed this weekend’s game, he would only be able to play limited minutes if he came to Australia, so the decision was made for him to stay in Scotland and continue his recovery."