Gregorius had a preliminary MRI exam on Sunday and was traveling back to the Yankees' spring training headquarters in Tampa, Fla., for further tests.
Yankees manager Joe Girardi told reporters Monday that the MRI revealed the 27-year-old Gregorius has a hematoma of the subscapularis muscle in his right shoulder.
"It's obviously not what you want to hear. Hopefully it's something short," Girardi said. "The evaluation from the doctor was his strength was really good, but we've got to see him. He'll have more MRI tests tomorrow."
Gregorius batted .348 (8-for-23) with four doubles, a home run and eight RBIs in six games to help the Netherlands advance to the WBC semifinals.
Girardi said the five-year veteran initially felt pain in his shoulder while throwing before Saturday's WBC exhibition game against the Arizona Diamondbacks.
"That's always your concern when guys play in the WBC, is they're not with you," Girardi said. "They're not in your hands and that's the hard part. I mean, arm injuries can happen, that's the bottom line. The thing is, he hasn't played a ton of defense."
Gregorius batted .276 with 20 home runs and 70 RBIs in 153 games for the Yankees last season, setting career highs in hits (155), doubles (32), homers, RBIs and extra-base hits (54).
Yankees general manager Brian Cashman told ESPN that even if Gregorius is out to begin the season, top prospect Gleyber Torres will not be the team's Opening Day shortstop.
Torres, 20, entered Monday hitting .444 in 27 spring training at-bats but is expected to start the season at Double-A Trenton.