Byrne missed two consultations to discover the severity of the problem and it is only now that the extent of the problem has been unearthed.
The British & Irish Lion will miss Heineken Cup rounds three and four but also the Magners League festive derbies with the Scarlets and Cardiff Blues.
Byrne could however, return to action for the league tie against Leinster on the weekend of January 7, a repeat of last year's Magners League Grand Final.
"We're now in a position to confirm the severity of the injury Lee suffered in the recent test match against New Zealand, which kept him out of the Edinburgh fixture last weekend," said Ospreys physio Chris Towers.
"Further investigations yesterday confirmed a fracture at the base of the thumb, and in light of this he is unlikely to be available for selection for an estimated period of five weeks from now."
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