The injury is not as bad as first feared after there were concerns Barmby had either snapped or ruptured the tendon.
"Nicky's injury is typical of what's been happening really," said Leeds boss Terry Venables. "It's one of those freak injuries.
"He was training, his studs got caught and he got a real bad pain down his Achilles. It didn't look good at the time, fortunately it's not ruptured or anything like that."