The team, which made the move retroactive to Thursday, said Eovaldi has two "loose bodies" in his right elbow. He has had two Tommy John operations and also had surgery last year to remove loose bodies in the elbow.
"It's just frustrating when you're coming off a good outing and you're taking the right steps forward, and you have to have this and you just can't throw," said Eovaldi, who informed the Red Sox on Thursday night that he could not straighten his right arm.
He had pitched six innings against the New York Yankees on Wednesday night.
Eovaldi and Dave Dombrowski, Red Sox president of baseball operations, said the injury appears to be similar to the one that sidelined the pitcher for the first two months of 2018.
It has yet to be determined whether more surgery is the best option.
"Don't know until the doctor takes a look at it," Dombrowski said. "He's going to see the doctor on Monday in New York, and we'll know more at that point."
Dombrowski described the problem as "just a very small piece in there, but it's in the wrong place."
Eovaldi is 0-0 with a 6.00 ERA in four starts. He allowed one unearned run and three hits in his last start.
Boston recalled left-hander Bobby Poyner from Triple-A Pawtucket to take Eovaldi's place on the roster. He has appeared in five games with Pawtucket this season, posting a 4.26 ERA.
Infielder Marco Hernandez is set to start a rehab assignment with Class A Salem. He didn't play last year following left shoulder surgery.
Infielder Brock Holt, out with a scratched right cornea, will remain on the injured list after his rehab assignment with Pawtucket.
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