Eovaldi, who is coming off a rough start in which he gave up five runs on nine hits in three innings against the Nationals, informed manager Mike Redmond that his back had tightened.
"His start is going to be in jeopardy tomorrow," Redmond said before Wednesday night's game. "It looks like he will probably be unable to go, and Flynn, we will move him up."
A September callup, Flynn has made one start, on Sept. 4 against the Cubs at Wrigley Field. The lefty gave up three runs on six hits in a no-decision that day.
Flynn is currently scheduled to start on Friday in the series opener against the Mets at Citi Field. But if he goes on Thursday, Brad Hand could get the nod on Friday in New York.
Hand has been slotted to pitch the second game of Saturday's doubleheader at Citi Field.
The hope is Eovaldi will be fine, and miss -- at the most -- a couple of days.
Sam Dyson is an alternative to start wherever he is needed.
Jose Fernandez will be shut down after Wednesday night's start, so he will no longer be part of the rotation. The Marlins have no intention of giving Fernandez more starts should Eovaldi be out an extended period.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter