Smith was struck on the side of the helmet by South Africa quick Anrich Nortje while batting on the morning of day four on Monday.
He was assessed on the field and passed a test, before reaching 27.
However Smith did not return when Australia began to field, with the vice-captain expected to undergo further assessment.
If Smith is diagnosed with a concussion, he would be ordered to enter a minimum 12-day mandatory stand-down period as he overcomes the symptoms.
That would rule Smith out of the second Test in Gqeberha starting next Sunday, but he could return for the third Test in Cape Town.
Josh Inglis is back on deck for Australia in South Africa as he returns from a fractured finger, and batted in the nets on Monday without issue.
Allrounder Cameron Green is also hopeful of returning from an abdominal strain in one of the final two Tests, but is unlikely to play a role with the ball.
Among all that Australia have a decision to make, in whether to retain Nic Maddinson at the top of the order or return Matt Renshaw there after his scores of 190 and 82 in Durban.
Smith has previously battled concussions, most famously when he was struck in the head by Jofra Archer during the 2019 Ashes.
On that occasion he also passed an on-field test at Lord's, before being ruled out mid-match and being replaced by Marnus Labuschagne.
The later head knock comes amid an eventful match for Smith.
He reclaimed the Test record for most career catches on Sunday with four takes in the field, including three brilliant moments in the slips.
The 37-year-old twice anticipated reverse sweeps from Temba Bavuma and Kyle Verreyne and moved early to put himself in a position to catch them off the middle of the bat.
Another take came when he leapt over in front of Matt Renshaw to remove David Beddingham, completing the catch with both feet in the air.
After being hit on the head on Monday, Smith recovered to three times beat a fielder at deep point off Nortje a few overs later.
He was eventually caught by the 203cm Marco Jansen on the long-on rope off Simon Harmer, having marginally cleared the quick on the boundary a few balls earlier.
It came as Australia went in search of quick runs on day four, allowing them to declare at tea on 6-314 and set South Africa 421 to win.
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