Oakley, who has only recently returned to training after illness, is set for another spell on the sidelines after suffering a hamstring injury.
Dons boss Neal Ardley told the club's official website: "We've had some bad news with George picking up a hamstring injury when we were doing some work on crossing and finishing in training (on Friday).
"We are fearful that it could mean a few weeks out for George. He was ill for a while and it's been a stuttering start to pre-season in terms of his physicality. We hope that it's not too serious."
However, some good news for Ardley sees Jake Nicholson back in full training after shaking off a hamstring injury.