Both Jones and Byrne could be available to Wales coach Warren Gatland ahead of Saturday's clash with South Africa.
"Sam Warburton has picked up an injury to his calf and as a result of scans today, he has been ruled out for two to three weeks," said Wales forwards coach Robin McBryde "
"It's disappointing because he really rose the occasion on Saturday. I thought he was outstanding and was a part of a combative back-row performance.
"But the positives are that Ryan Jones and Lee Byrne took part in training."
The return to training of Jones will soften the blow of losing Warburton, who was so impressive against the Wallabies last weekend.
"I managed a jog on Monday and took part in training yesterday," said Jones.
"It's so far so good and I've had no reaction. I got through training and like to think I held my own. I feel good in myself, I'm confident and if I do get an opportunity this weekend I'm going to take it."
Scarlets rookie George North has also returned to full training and will win his first cap if selected to face the Springboks. The 18-year-old played more than an hour in the Scarlets 52-13 demolition of Leeds Carnegie in the LV=Cup on the weekend.