Ashley-Cooper, who has been a revelation for the Wallabies this season, was forced from the training paddock during the last day of the squad's week-long camp in Portugal with a groin complaint.
He joins prop Guy Shepherdson (knee) as the Wallabies' other main injury concern, while reserve flyhalf Berrick Barnes has started running freely and appears to be nearing full fitness after his groin injury.
"Adam showed a lot of maturity the other day," said Wallabies defence coach John Muggleton.
"He felt a bit of a twinge and a bit of tightness in the groin and he went and saw the medical staff straight away.
"Berrick's is an on-going one that has been treated by the medical staff over a period and he is progressing terrifically - today he can go out on the field and can run through the stuff without over extending himself, so that is a great thing to have him back in team session."
Shepherdson's injury is of more concern for the Wallabies staff. The big tight-head prop was unable to train with the team during the camp in Sydney last week and was hoping to prove his fitness in Portugal.
But his injured knee swelled up on the lengthy flight to Europe which has hindered his preparation in Portgual. However, the 25-year-old is confident he will overcome the injury.
"It has been frustrating," Shepherdson said. "But the medical staff are confident in the treatment of the injury and that gives me confidence.
"I haven't had to deal with an injury like this before but they (the medical staff) seem to think it will be fine, so that gives me confidence that everything will be alright."