"Unfortunately with J.B., that play in Atlanta he rolled the ankle and it wasn't getting any better," Marlins president of baseball operations Michael Hill said. "We opted to DL him, and allow him to take the time to rest it."
Bour twisted his ankle Saturday in Atlanta, and he hasn't played since. The left-handed-hitting first baseman, who has 15 home runs and 46 RBIs, is on the DL retroactive to Sunday, and he is eligible for reinstatement on July 18, which would be the series opener at Philadelphia.
Marlins manager Don Mattingly played one man short on Tuesday as Bour returned to Miami to have an MRI.
"You have the All-Star break [coming up], but you don't want to have Donnie playing short for any amount of time," Hill said. "With the high ankle sprain, you know it's going to take the week to 10 days."
Kelly, 36, started at first base for Miami on Wednesday in the series finale against the Mets at Citi Field.
This past year, Kelly has dealt with his own injury issues.
After making the Marlins' Opening Day roster in 2015, he received just one at-bat, on April 12. But on that day, he fractured a bone on his finger.
Shortly after recovering from his finger injury, Kelly injured his right elbow, which required Tommy John surgery last July.
"I feel great," Kelly said. "Finally, I feel 100 percent and feel healthy. It's good to feel that way, and good to be back with these guys."
In 48 games at New Orleans, Kelly was batting .223/.288/.273 with one home run and 12 RBIs.