Davies appeared to sustain the problem in the early stages of Clermont Auvergne's 35-3 European Champions Cup victory over Sale, and had to be substituted following their first try.
Although the 26-year-old travelled to meet up with Warren Gatland's Wales squad on Monday, it was confirmed he would play no part in training as they look to discover the extent of his injury.
"Jonathan had a bump on his shoulder and we are uncertain as to the extent of the injury," coach Rob Howley told a media conference.
"A scan has been organised for him.
"I watched the game. He created a fantastic try after he had done something to his shoulder. He has obviously felt some pain and come off immediately. We just have to wait to ascertain how bad that injury is.
"It's disappointing, but centre is a pretty attritional position now. It's the nature of the game. It's no different to other campaigns. We just have to get on and work with what we've got."
The news will be a blow to Gatland, who already has injury concerns over Scott Williams and Cory Allen ahead of Wales' matches with Australia, Fiji, New Zealand and South Africa next month.