Red Sox manager John Farrell said Price underwent an MRI and the results were inconclusive, though Price has shown improvement since Wednesday and the injury isn't thought to be serious, per Pete Abraham of the Boston Globe.
According to Tom Caron of NESN, Price will get a second opinion on the ailment.
Michael Silverman of the Boston Herald added that Price is set to visit Dr. James Andrews.
Per ESPN's Jim Bowden, Farrell said there is concern regarding the injury since the soreness is more extensive than it had been in the past. Bowden also reported there is "serious concern" Price could be a candidate for Tommy John surgery.
Price has been durable throughout his career. He's avoided any major injury setbacks, making at least 27 starts in seven straight seasons at a time when arm and shoulder injuries are a consistent concern. It made him a safer investment when the Red Sox signed him to a seven-year deal last offseason.
Any issues he's dealt with have been of the more manageable variety. That includes a minor hamstring injury he was able to fight through in 2015 when he posted a 2.45 ERA in time spent between the Detroit Tigers and Toronto Blue Jays.
While losing Price would be a significant blow, the Red Sox currently have more quality starting pitching depth than they've had in years.
In addition to the return of reigning AL Cy Young Award winner Rick Porcello as well as Steven Wright, Drew Pomeranz and Eduardo Rodriguez, Boston acquired five-time All-Star Chris Sale from the Chicago White Sox in an offseason trade.
The 2016 season was a roller-coaster ride for Price as he posted an uncharacteristic 3.99 ERA despite winning 17 games and posting 228 strikeouts.
Price is among the most dominant southpaws in the league when on his game, though, and Boston will miss his presence if he is out for a significant period of time.