MLB Network's Jon Morosi first reported the move.
The news comes after ESPN.com's Buster Olney reported Price underwent an MRI on Thursday.
It's been a rocky season for Price on the injury front, and the latest ailment only stands to complicate matters.
After Price's season debut was delayed until May 29 due to elbow troubles, he was bothered by a blister and split fingernail on his pitching hand.
When healthy, the southpaw has gone 5-3 with a 3.82 ERA and 2.86 strikeout-to-walk rate during his second season in Boston.