Smith was struck on the neck by a Jofra Archer bouncer during his innings on Saturday, forcing him to retire hurt, but he returned to the crease 40 minutes later and added 12 runs before being dismissed for 92.
“Steve Smith has been closely monitored by medical staff overnight,” Cricket Australia said in a statement.
“He slept well but woke up with a bit of a headache and feeling of grogginess.”
“As part of the Cricket Australia concussion protocol, repeat testing was performed this morning and demonstrated some deterioration, which is consistent with the emergence of the symptoms he was reporting. On that basis, he has been withdrawn from the match.”
Smith, who made 144 and 142 in Australia’s first-test victory, did not field at the start of England’s second innings on Saturday and will play no part in the last day of the match.
England resumed on 96 for four on Sunday after a rain delay of over an hour, leading by 104 runs.
Smith, who was also hit on the forearm during a hostile spell by Archer, will be assessed ahead of the third test in Leeds starting on Thursday.
“In terms of his availability for the next test, it will be considered over the coming days but the short turnaround is not in his favour. He will be assessed on an ongoing basis and will have a precautionary scan on his neck on Sunday,” Cricket Australia said.