The 32-year-old stumbled badly after making a tackle early in the All Blacks' 54-34 victory in Sydney. He appeared disorientated then was involved in two more heavy collisions before play stopped.
However, he was not checked out by the team's medical staff or the independent doctor employed to assess head injuries.
News Corp Australia said on Tuesday that SANZAAR had opened an investigation after reviewing footage of the incidents.
SANZAAR did not immediately respond to calls from Reuters.
Williams appeared lucid in a television interview after Saturday's game and All Blacks coach Steve Hansen said the following day that no one had noticed him suffering any adverse effects from the collisions.
"I think everyone missed it to be fair, otherwise the HIA doc would have taken him off," Hansen told reporters referring to the Head Injury Assessment personnel.
"Our doc certainly would have taken him off."
All Blacks assistant coach Ian Foster said that Williams had not been pushed at training on Tuesday as a precaution but presented with no symptoms.
"Sonny took a knock in the weekend but he was symptom-free," Foster told reporters in Dunedin.
"The Doc has done what he always does when there is a suspicion of something. He was held back a little bit today so we could make sure he was absolutely clear but the signs are really positive."
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
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