The 32-year-old did not take the field on Saturday morning and will not bowl on day four as the match looks destined for a draw.
It is understood the injury is not too serious and that Bollinger, who played the last of his 12 Tests in Adelaide against England in 2010, is being rested as a precaution.
The big left-armer is back in contention for an Ashes Test spot against England after injuries to fellow quicks Mitchell Starc, Ryan Harris, James Pattinson, Jackson Bird and Pat Cummins.
Australia's squad for the first Ashes Test starting on November 21 in Brisbane will be named on Tuesday.
Meanwhile, Test opener Chris Rogers reached his century with a sweep shot off Nathan Lyon's second delivery of the day.
The veteran fell for 117 midway through the rain-interrupted morning session when he spooned an easy catch to mid-on off Lyon's bowling.
He was the only batsman to fall before lunch as the hosts progressed to 2-250, leading by 133 runs with two sessions to play.