The 25-year-old made his comeback from the pectoral injury for the Scarlets against London Irish at the start of February.
He has returned to the Wales squad, but was not one of the players released back to the regions for the weekend's Pro12 matches.
"It was great to get back on the field against London Irish for the Scarlets a few weeks back - but afterwards the injury was still a bit sore after half and hour of action," Davies told the Carmarthen Journal.
"The advice was just to take my time and not push it, to make sure I've recovered fully. It's difficult because you just want to play, but it really isn't worth risking it.
"I was assessed after the game by the medical teams and they said I just needed to take it easy for a week or so and then build up again gradually.
"But I'm still working hard in training. As a precaution they are keeping me away from full contact training and I'd hope to have some game time with the Scarlets again soon.
"It's a test of your mental strength more than anything else and you just have to be patient."