The Red Sox placed Wright on the 10-day disabled list with a sprained left knee that has been bothering him since spring training on Tuesday.
"He felt like there was a spike in the discomfort," said Red Sox manager John Farrell, per Browne. "He was obviously taken for an MRI at that point, and it's more severe than what he had been dealing with at any point and time. Like I said, we're still gathering information."
An All-Star last season, Wright was a mess to start 2017 with an 8.25 ERA and 40 hits allowed in 24 innings.
The Red Sox are already lacking starting pitching depth with David Price on the disabled list. Reigning American League Cy Young winner Rick Porcello is also off to a slow start with a 4.46 ERA.
Kyle Kendrick will make a spot start in Boston's rotation on Thursday in place of Wright.