Recalled Taine Basham would be the leading contender to replace Wainwright on Saturday, with Scarlets back-rower Taine Plumtree providing the other option in the squad.
Basham was rewarded with a squad call-up having been the form number eight in Welsh domestic rugby this season.
The Cardiff number eight has not played for Wales since the 2024 Six Nations, while his previous start to that was in 2022.
After the All Blacks match, Wales will host Australia on 21 November, before the Nations Championship finals weekend at the end of the month, hosted by the Allianz Stadium at Twickenham.
Wales currently lie fifth out of sixth in the northern hemisphere table after two wins from four matches.