Manager Joe Girardi said that Tanaka, who issued a statement on Friday apologizing to the Yankees and their fans for the injury, would prefer to skip the trip to Minneapolis and focus on his rehabilitation.
"I think it's really unfortunate, because he had a great first half and he's not able to be a part of it," Girardi said. "But for some reason, I think he's going to get a chance to be a part of another one."
Tanaka, 25, was selected as an American League All-Star after going 12-4 with a 2.51 ERA in 18 starts. Following the injury, Red Sox manager John Farrell replaced Tanaka on the AL squad with Boston reliever Koji Uehara.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.