Williams endured two big hits during his side's victory but was reportedly not checked by medical staff to assess for a head injury.
Concerns over whether Sonny Bill Williams should have had concussion test during New Zealand's win over Australia in Rugby Championship
Southern hemisphere rugby's governing body (SANZAAR) is looking into whether medical officials should have conducted concussion tests on New Zealand centre Sonny Bill Williams during Saturday's Rugby Championship opener against Australia.
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.
Read Paul Radley's series on concussion
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.
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."
Meanwhile, New Zealand hooker Dane Coles is expected to make his return to test rugby on Saturday against Australia in their Rugby Championship, ending a frustrating five months battling injury.
Coles missed last weekend's 54-34 victory over the Wallabies in Sydney as a precaution after picking up another head knock in a troubled season for the Wellington Hurricanes captain.
The 30-year-old last played a test nine months ago and since mid-March has played just 90 minutes in the Super Rugby playoffs for the Hurricanes due to lingering concussion symptoms.
He was injured again in the All Blacks' 'Game of Three Halves' warmup match against provincial sides Taranaki and Counties Manukau and immediately ruled out of last week's game, which doubled as this year's Bledisloe Cup opener.
All Blacks assistant coach Ian Foster, however, said Coles had been impressive in his return to training and was back in contention for Saturday's clash in Dunedin.
"He trained really well," Foster said. "He had a good week last week actually.
"He's come through today really well."