The former Auckland and Chiefs utility suffered a shoulder injury in the November game with Australia.
It is a shoulder blade injury where the time for recovery is affected by the bone growth achieved. Wales captain Justin Tipuric suffered a similar injury playing for the British & Irish Lions against Japan in 2021 and missed a complete season.
For Anscombe, however, the injury after another saw him miss the 2019 Rugby World Cup. That was during a two-season layoff for a knee injury that required two operations involving a realignment of his leg and a bone graft from a donor.
Once over that, he regained his place in the Test side and kicked Wales to their first win over South Africa on African soil in July.
Having transferred from the Cardiff Blues to the Ospreys, Anscombe is off contract at season's end and is considering options for his future.
French side Pau and several Japanese clubs are interested in him, but he has said his immediate focus is on regaining his fitness.
Meanwhile, Chiefs No8 Pita Gus Sowakula, who played two Tests for the All Blacks against Ireland this year, has confirmed he has signed with Clermont on a two-year deal with a third-year option.
He will take up the role after the 2023 Super Rugby and NPC seasons.