The Clermont Auvergne full-back was hurt just before half-time of his team's Heineken Cup victory over reigning European champions Leinster in Dublin on Friday.
The French club, on their official website, said 32-year-old Byrne had "suffered a fractured right pedicle of the fifth lumbar vertebra".
Byrne, who has won 46 Test caps and toured South Africa with the 2009 British and Irish Lions, is in his second season of a three-year contract with Clermont.
He was not part of the Wales squad that played autumn internationals against Argentina, Samoa, New Zealand and Australia last month, losing all four games.
- Sports & Recreation
- Clermont Auvergne
- Heineken Cup
- British and Irish Lions