The England international sustained the problem during the warm-up ahead of the game with one of his former clubs, Tottenham, in November.
As Barmby has suffered a partial tear of his tendon, he required surgery at the end of last week, in an attempt to fix the problem.
Consequently, the former Liverpool and Everton man will be sidelined for at least a further eight weeks, as he recovers and then bids to return to full fitness.
It is a blow to manager Terry Venables, whose side missed out on a confidence-boosting second successive win on Saturday when Southampton snatched a late equaliser at Elland Road.
