"Bradley will have an operation early next week and an accurate timescale on his recovery will be assessed after the operation," read a Blues statement.
Wales have already lost Alun Wyn Jones (shoulder) and Luke Charteris (knee). Charteris is out for the rest of the season, but Jones could return mid-way through the RBS 6 Nations.
Davies' woes continue after he missed most of Wales' 2012 campaign after he was banned for a tip tackle in their opening match against Ireland while he was felled by New Zealand's Andrew Hore in the autumn internationals and missed the clash with Australia.
Cardiff Blues' Lou Reed, winning his second cap, and Charteris started against the Wallabies after Ian Evans was ruled out.
Versatile back-five forward Ryan Jones then replaced Charteris early in the second period.
Evans has yet to reappear for the Ospreys, who announced on December 6 that he faced a six-to-eight-week lay-off.
Ryan Jones and Reed are now contenders to continue their partnership against Ireland, who are themselves without experienced British and Irish Lions lock Paul O'Connell.