Meyer faced three batters and threw only 10 pitches before being removed in the first inning of his start Saturday against the Pittsburgh Pirates.
The third overall pick in 2020 draft, the 23-year-old Meyer made his major league debut last Saturday and was making his second career start in Pittsburgh.
Meyer's injury was one of many the Marlins announced Sunday. Third baseman Brian Anderson (shoulder sprain) and right-handed reliever Tommy Nance (right groin sprain) were placed on the IL along with Meyer, while second baseman Jazz Chisholm Jr. (stress fracture in back), reliever Anthony Bender (back) and reliever Cody Poteet (right elbow inflammation) were all transferred to the 60-day IL.
In corresponding moves, Miami called up infielder Willians Astudillo and right-handers Huascar Brazoban and Jeff Brigham from Triple-A Jacksonville.