Chen is expected to miss only one turn. He allowed two runs over six innings with seven strikeouts Monday against Tampa Bay and is 2-1 with a 4.33 ERA in five starts this season.
"He threw his bullpen yesterday. To us it looked pretty good, but he felt like he couldn't make his next start, and at that point we were like, OK, send him back to Miami to see the doctors and we kind of expect him to be able to make it," Marlins manager Don Mattingly said following Friday night's 8-7 loss to the Mets.
"He just felt like it was kind of dead, and at that point we had to -- he didn't think he could make the start."
Mattingly said he wasn't sure whether Chen had an MRI.
Chen signed an $80 million, five-year contract with the Marlins as a free agent before last season. He went 5-5 with a 4.96 ERA in 22 starts during his first year in Miami, missing two months with a sprained left elbow.
Right-hander Jose Urena is scheduled to make his first start of the season Sunday in place of Edinson Volquez, on the DL with a blister on his right thumb. Urena has a 2.35 ERA in six relief appearances this year.
Despaigne missed much of spring training with a strained left oblique and began the season on the DL before getting optioned to Triple-A. He is 9-18 with a 4.89 ERA in 69 big league games, including 34 starts, for San Diego, Baltimore and Miami. He hasn't started in the big leagues since 2015 with the Padres.