Rogers, unbeaten on 44 overnight, added five runs before signalling to the dressing-room that he was feeling unwell.
The 37-year-old left-hander sunk to his knees and was treated by medical staff before walking off the field looking groggy.
He was replaced at the crease by Steve Smith with Australia on 114 for no wicket in their second innings, 368 runs ahead of England.
Rogers was struck on the helmet by James Anderson off the first ball of the second day of the match but recovered to score 173 in Australia's first innings.
He also missed two tests in West Indies recently after receiving another blow on the head.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
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