Mooy has not featured since appearing as a substitute in the 2-0 win over Hearts on May 7 that clinched the Scottish Premiership title with Celtic failing to win in the three matches that have taken place since, losing to Rangers and Hibs either side of a draw with St Mirren.
The 32-year-old has been an influential performer since returning from the World Cup with Australia, scoring seven times and registering six assists in the second half of the season as Celtic wrapped up the title.
But he has been struggling with a back injury in recent weeks and has managed just one start since mid-March with manager Ange Postecoglou confirming he is unlikely to feature at Hampden next Saturday as Celtic bid to secure the treble against Inverness.
“Aaron Mooy is still struggling with a back complaint so he will miss out and is probably a doubt for cup the final," he said.
Right-back Alistair Johnston is set for a comeback from injury in the final league match of the season against Aberdeen on Saturday. However, Sead Haksabanovic will miss out after picking up a knock in the 4-2 midweek defeat to Hibs.
On Johnston, who suffered a leg knock in the Scottish Cup semi-final against Rangers, Postecoglou said: “He is good to go. He will play on Saturday and if he gets through that then we will see for the cup final.
“Sead, who came off the other night, is not as bad as we thought. He will miss Saturday but we think he has a good chance for the cup final which is good for him and good for the group.”