The in-form 25-year-old is in the Socceroos squad for the big World Cup 2018 qualifiers against Iraq and the United Arab Emirates.
The first match takes place in Perth on Thursday (11.30am British time) and the second in Abu Dhabi the following Tuesday (4.30pm British time).
Mooy, who is on loan from Manchester City, will then return ahead of Town’s next Championship game at Leeds United on Saturday week, September 10.
The former Melbourne City man has played a key role in Town’ successful start to the season under David Wagner.
Two points clear at the top of the table, they will seek a fifth win in game six of the campaign at Elland Road.
Iga, Town’s head of performance services, said: “Obviously there’s a lot of travelling involved for Aaaron.
“By talking to my counterparts at the Australian national team, we can compare data and work out the best way for Aaron to prepare and recover for the two games.
“The aim is to get him back as fresh as he can be.”
It’s the start of the third phase of Asian confederation qualification for 2018, with the Socceroos in a group which also includes Japan, Saudi Arabia and Thailand.
There are home and away games running through to this time next year.
The top two in each of the two groups qualify for the finals.
The two third-placed sides will play each other home and away to determine which takes part in an inter-federation play-off against a nation from CONCACAF (North, Central American and Caribbean).