The Munster flanker is still awaiting results of scans after he suffered the injury on Monday during training.
Coach Joe Schmidt will be eager to see him in action, with O'Donnell's fellow back-rowers Jack Conan and Dan Leavy both struggling with injury.
Ireland take on the Springboks in Dublin on Saturday and Rhys Ruddock may now get his chance on the bench.
British and Irish Lions trio Sean O'Brien, CJ Stander and Peter O'Mahony could be a potential starting back row and forwards coach Simon Easterby admits Ireland have a few selection headaches.
He told reporters: "Tommy O'Donnell picked up a bit of a shoulder bump in training on Monday so he's due to have a scan at some point today [Tuesday].
"Jack Conan sat out training, he just had a heavy workload. Dan Leavy had a bit of tightness in his hamstring, obviously he played at the weekend. Again it's just managing his workload.
"It's just about being sensible and earmarking players who may have potential weaknesses. If you know about things, at least you can prepare for that and not take any unnecessary risks."