Davies went down in the closing seconds of the 29-21 loss in Cardiff and received treatment on the pitch after the final whistle had been blown.
The Welsh Rugby Union confirmed on Wednesday that the issue would require surgery, placing a six-month estimate on his recovery.
Davies' injury means he will miss next year's Six Nations, as well as the majority of the remainder of the Scarlets' season, as the men from Llanelli look to build on last year's Pro12 triumph.
His absence also comes as a blow to Warren Gatland's hopes of implementing a new style of play with Wales, having started Davies alongside Owen Williams for the first time against the Wallabies.
Veteran centre Jamie Roberts was called into the squad as cover on Monday, while the experienced Scott Williams is also involved, having initially been omitted by Gatland.
Wales faces Georgia on Sunday, before taking on New Zealand and South Africa over the following two weekends.