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.
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.
--The Cincinnati Reds named right-hander Scott Feldman as their starting pitcher for Opening Day on April 3 against the Philadelphia Phillies.
Feldman earned the nod over left-hander Brandon Finnegan, who will start the second game, manager Bryan Price announced Monday.
Feldman will be opposed by right-hander Jeremy Hellickson, who was named the Phillies' Opening Day starter on Sunday.
Tiger Woods continues to struggle with back issues but the 14-time major champion has not ruled out playing the Masters in two weeks.
"God, I hope so," Woods said when asked by "Good Morning America" host Michael Strahan if he would be able to play in the upcoming Masters. "I'm trying. I'm trying every day to get back and play."
Woods appeared on the ABC show in New York to promote his new book, "The 1997 Masters: My Story." He won the first of his majors 20 years ago at Augusta National by a record 12 shots at age 21.
Woods has not played a golf tournament since back pain caused him to pull out of the Omega Dubai Desert Classic on Feb. 3.