Parry is an experienced campaigner who last played for Wales in the 52-16 World Cup warm-up game against South Africa.
He was left out of the final squad for the global tournament with Gatland taking Lake, Dee and Elias to France.
Parry was not included in the Six Nations but had been called up to the summer training squad.
Gatland had stated he would cut the final Australia touring party to 34 after the match against South Africa.
Wales will play Test matches in Sydney and Melbourne next month alongside a friendly against Queensland Reds in Brisbane.
Parry’s departure provides further disruption to Wales’ summer preparations with Jac Morgan, Taulupe Faletau, Tomos Williams, Adam Beard, Teddy Williams, Rhys Davies, Joe Roberts, Leon Brown and Josh Macleod missing through injury, Will Rowlands and Josh Adams rested and Gareth Anscombe making himself unavailable as he recovers from long-term injury.
English-based club players Dafydd Jenkins, Tommy Reffell, Nick Tompkins, Dillon Lewis, Archie Griffin, Christ Tshiunza and Josh Hathaway are unavailable for the South Africa match because it falls outside World Rugby’s international window but should return to face the Wallabies.
Prop Henry Thomas was ruled out of the South Africa match because of a foot injury but hopes to be fit to travel to Australia.
