Assistant coach Jason Ryan said the veteran second-row forward sustained a head knock after replacing skipper Scott Barrett in the 56th minute in Cordoba last Saturday.
"Patty went off to hospital and had a couple of check-ups as well, which we are monitoring over the next 24 hours," Ryan said from South America. "Patty is potentially unlikely for this week."
Ryan said Barrett had been withdrawn from the contest to manage his return from an achilles injury, and would be fit for Saturday's clash in Buenos Aires.
Fabian Holland, who started alongside Barrett in the second row, has also been given a clean bill of health despite being taken off with cramp late in the Cordoba clash.
Ryan said number eight Wallace Sititi and loosehead prop Tamaiti Williams could be available for Saturday's match after missing New Zealand's tournament-opener as they continue to recover from ankle and knee operations respectively.
"We have got some decent selection decisions ... because the people in those positions are playing pretty well. That's healthy," Ryan said.
The hard-fought victory over Argentina, combined with Australia's stunning upset of world champions South Africa, will send the All Blacks back to the top of the world rankings for the first time since 2021.
The Springboks will drop from the top spot they have occupied for most of the past five years to third behind Ireland. The Wallabies will remain in sixth behind France and England.
"It just shows you how tough Test footy is, how close it is, and the margins," head coach Scott Robertson said in a post-match news conference in Cordoba.
"We're pleased we're number one, but our sights will probably be more set on next week's match than rankings."
