Ireland coach Declan Kidney insisted his withdrawal was just a precautionary measure.
"Brian was feeling a bit off so it was prudent for him not to train. You know when you just don't feel good in yourself," said Kidney.
"He's not feeling great so there was no point pushing it on a day like today so he's back in the hotel resting up.
"Two weeks ago against France we had a few lads who didn't take part in the captain's run.
"The Captain's Run is just to blow a few cobwebs out after the travelling. In some cases it's better for a player not to train and that was the situation with Brian.
"We're quite hopeful that he'll be alright for tomorrow."
Kidney added: "I'm going to bed thinking he will wake up tomorrow looking forward to the game and that's what the medics say too."
Should O'Driscoll fail to recover, Keith Earls will switch from the left wing to outside centre, Andrew Trimble will take the number 11 jersey with Paddy Wallace drafted on to the bench. Paul O'Connell would also step in as captain.
Flanker Stephen Ferris, who returned from a knee injury in the 33-10 defeat by France a fortnight ago, also sat out the Captain's Run.