Faletau fractured his forearm in Bath's clash with Exeter Chiefs in October and suffered a recurrence of the injury upon returning to action in January.
The 28-year-old was initially thought to have a chance of featuring in Wales' final match against Ireland, but further surgery means he is unlikely to play any part.
"We're gutted for Taulupe, but this is the best course of action for him moving forwards as a player," said Bath director of rugby Todd Blackadder.
"We will know more in terms of timeframes following the surgery, but we're looking forward to welcoming him back into the squad."
There was a boost for Wales on Tuesday, though. Leigh Halfpenny (concussion) and Rhys Patchell (hamstring) are expected to be in contention when Wales host England at the Principality Stadium on February 23.