In his second career start, Meyer faced just three batters and threw 10 pitches before exiting after being met on the mound by manager Don Mattingly and an athletic trainer.
The 23-year-old Meyer made his debut last Saturday, losing to Philadelphia at home. The Marlins selected him third overall in the 2020 draft.
Earlier in the day, the Marlins placed left fielder Jorge Soler, last year's World Series MVP with Atlanta, on the 10-day injured list with back spasms. In his first year with Miami, Soler is hitting .207 with 13 home runs in 72 games.
JJ Bleday's contract was selected from Triple-A Jacksonville. The outfielder was the fourth overall pick in the 2019 draft out of Vanderbilt and was looking to make his big league debut.
The Associated Press contributed to this story.