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Smith was on 80 when he was hit on the neck by test debutant Archer, who bowled a hostile spell from the Pavilion End during which his deliveries reached speeds of well over 90 miles per hour.
Smith, who made 144 and 142 in Australia's emphatic victory in the first test, had defied the England attack again as the touring side replied to the hosts' first-innings total of 258.
He was given a standing ovation by the crowd at the home of cricket as he walked off the ground before returning to the crease about 40 minutes later following the dismissal of Peter Siddle.
"Steve was hit on the neck below the left ear," Cricket Australia said in a statement. "He was assessed lying on the pitch at the instructions of team doctor Richard Shaw.
"Dr Shaw made the precautionary decision to remove Steve from the field of play to have him further assessed under Cricket Australia's head impact protocol. Steve then passed his assessments and will now be monitored on an ongoing basis, as is routine."
Smith, who was also struck on the arm by another Archer delivery, showed he was suffering no serious ill-effects by hitting Chris Woakes for successive boundaries, but he misjudged a straight ball from the same bowler and was adjudged lbw for 92.
He reviewed the decision but walked towards the pavilion as the replays were being studied by the video official who confirmed that the ball would have hit the stumps.
Smith did not come out to field at the start of England's second innings. Cricket Australia said he had suffered a bruised left forearm and had gone for a precautionary X-ray.
"It's hard to watch, he's in good spirits tonight and he passed all the concussion protocol," Australia coach Justin Langer said.
"It was a nervous time. He'll have another test for concussion in the morning, thankfully his arm is OK as well. He is an incredible player and as long as he passes the guidelines I am sure he will be out there tomorrow.
"There is no way we would have let him come back out if he wasn't healthy."
Former Australia batsman Phillip Hughes died after being struck by a bouncer in the neck during a first-class match in Sydney in 2014.
It was the seventh Ashes innings in a row that Smith has passed fifty, a record in test matches between England and Australia.
The former Australia skipper was stripped of the captaincy and served a 12-month ban for his role in a ball-tampering scandal during the test series in South Africa last year.