The Wales full-back left the Stade Aime Giral on crutches and will find out if he is ruled out of Wales' title defence following a scan later today.
Byrne has been in superb form this year, starring for both club and country and putting his name forward as the leading contender for the Lions No15 shirt.
"We will assess Lee's injury when he has a scan," said Ospreys coach Jon Humphreys.
"It's very painful at the moment but until the doctors have a look at him, we can't rule him in or out.
"He's strapped up and on crutches. We hope he will be fit for next week and we will give him the best possible chance."
It will be a major blow for Wales coach Warren Gatland if Byrne, rated as the number one full-back in the world on form, is ruled out of the opening Six Nations clash with Scotland at Murrayfield on February 8.