The team is weighing who will take over Sanabia's spot in the rotation, which next comes up on Friday at home against the Mets.
Manager Mike Redmond on Monday said Wade LeBlanc, who opened the season in the rotation before being moved to the bullpen, is an option.
Redmond ruled out Nathan Eovaldi, who is on the 60-day disabled list with right shoulder inflammation. Eovaldi threw a rehab assignment game at Class A Jupiter on Saturday.
"Right now, he's scheduled to make two more starts down in the Minor Leagues," Redmond said. "We've got to make sure he is built up properly, and is feeling good before he comes back to the big leagues."
Injuries keep piling up for the Marlins, who currently have 12 players on the disabled list.
Sanabia threw four innings and gave up four runs in Sunday's 5-3 setback against the White Sox. Immediately after the game, he told reporters that he would be heading to the disabled list.
Sanabia has dealt with a sore groin since his start early in the month at San Diego. The right-hander is 3-7 with a 4.88 ERA.
Because the Marlins won't need another starter until Friday at home against the Mets, the team called up a reliever. Jennings, 26, is 3-2 with a 1.80 ERA for New Orleans. He has a 0.68 ERA in his last 10 outings.
Jennings, who has always relied heavily on his slider, attributes some of his success in New Orleans to fastball command.
"I'm able to throw my fastball on any count, and working both sides of the plate," Jennings said. "I've been able to throw my fastball better than I have in the past."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter