The pitcher was sent home and will undergo tests on the injury.
Rick Porcello, who was supposed to start Thursday, will move up one spot and take Price's place.
Unfortunately for the Red Sox, medical woes are nothing new for Price. The southpaw missed the first two months of the 2017 campaign with a left elbow strain, and he was sidelined later in the year because of inflammation in the same elbow.
Through seven starts in his third season with the Red Sox, Boston's $217 million man has gone 2-4 with a 5.11 ERA, 1.41 WHIP and 2.0 strikeout-to-walk ratio. He allowed seven earned runs in 3.2 innings in his most recent start, a loss to the Texas Rangers last Thursday.
The American League East contenders have the depth to survive a short-term absence from Price, to be sure, but they'll need him back at 100 percent if they want to maintain a grasp on the top spot in the division. Boston entered Tuesday's game with a one-game lead over the Yankees.