The Wales international strained his hamstring during the Lions' 47-17 victory over New South Wales Waratahs two days ago.
"Jamie is a grave doubt for this week, there is no doubt about that," said Lions team doctor James Robson.
"You only had to see how much discomfort he was in at the weekend.
"However, further assessment will be made later in the week as to his availability going forward."
Robson, though, was more upbeat about wing George North, who is battling to overcome a hamstring complaint.
"George is an exceptional character and has worked really hard," Robson added.
"He is back to running today [Sunday]. He is doing very, very well.
"An accurate assessment of his availability for selection will take place on Wednesday, but at the moment I think he is doing very well."
The Lions face the Brumbies in Canberra on Tuesday, with head coach Warren Gatland due to announce his first Test team on Thursday.