Barnes took an accidental knee to the back during the 60-11 triumph at English Rugby's HQ and was forced off the field late in the first half.
And while the Wallabies coped without the 25-year-old against the invitational XV, losing Barnes for another 80 minutes would be a big blow.
Barnes won the man-of-the-match award when Australia beat Wales in the Bronze Medal clash at the recent World Cup in New Zealand and his importance to the side has grown since Quade Cooper's serious knee injury.
Cooper is currently sidelined for around six months following ACL surgery, leaving Barnes and James O'Connor to become central figures in Australia's attacking game plan.
If Barnes does prove his fitness, head coach Robbie Deans is not expected to make any changes to the backline but if he fails to recover in time, Reds centre Ben Tapuai could make his first international start having replaced Barnes on the first game of the two-match tour.
No.8 Ben McCalman is set to return from an eye irritation that ruled him out on the morning of the Babaas fixture and captain James Horwill is likely be promoted to the starting lineup having been rested on Saturday.