The lay-off means the 31-year-old will miss Ulster's upcoming Heineken Cup double header against Benetton Treviso as well as their festive derby clashes with Leinster and Munster.
Mark Anscombe's men currently hold a two-point lead at the top of their European pool and they wrap up the pool stages against Montpellier (home) and Leicester Tigers (away) in January, by which time Best would ideally be back playing.
"I'm in for an operation tomorrow morning (Tuesday) and hopefully (the recovery) will be around about eight weeks," Ireland's most-capped hooker told BBC Northern Ireland.
"I think a realistic target would be rounds 5 and 6 of Europe, well that's certainly my target. But we won't know until (the surgeon) Michael Eames goes in and sees the exact extent of the damage."
Best was heavily involved in Ireland's thrilling start to the All Blacks, scoring a fine try - his eighth score in 70 Tests - before the damage to his right forearm forced him off in the 15th minute.
Before he was replaced, the 2013 Lion actually played on with the injury - getting back in the defensive line and cleaning out a ruck until the ball went dead and he could receive treatment.
Recounting the moment when the fracture took place, he revealed: "I was making a tackle on the New Zealand number 6 Steven Luatua. As I hit him Paul O'Connell went to hit him as well and just as soon as it happened I heard a bit of a thud, a bit of a crunch.
"When I looked down, my hand was just hanging limp, I had no real control of it and there was just a throbbing. So I knew straight away.
"Unfortunately there was a bit of a while before there was another break in play and the ball went off and I could get a bit of treatment. To be honest, as soon as it happened it was just a matter of time before I had to leave the pitch."
Although disappointed with the prospect of missing the next two months of the season, Best was thankful of the care he received from the Ireland medical team on site and the fact that the injury was not worse than it was.
"I'll be pushing hard to get back for European games in January, the surgeon thinks that's a realistic goal. It's disappointing to be injured and to go off so early on Sunday. But at least it's not completely horrendous news.
"It's given me a good realistic target to work for and hopefully now we can be in a position, in those last two games, to make sure we get that home quarter-final which is what we all want.
"The good thing about the medical care at the Aviva (Stadium), they X-rayed it. So I was injured, X-rayed and back out to pitchside before half-time so they don't mess around. They put a small bit of a cast on just to keep it steady and take away a bit of the pain," he added.
* A statement issued by Ulster Rugby today confirmed that Best underwent successful surgery in Belfast this morning to stabilise the fracture that. He is expected to return to rugby in mid to late January.
Meanwhile, fellow forward Iain Henderson had an MRI scan yesterday on the hamstring injury that he suffered in Ulster's win over Edinburgh last Friday. The scan confirmed that he has a hamstring tear and he will be out of rugby for up to six weeks.