Simpson (elbow) is scheduled to begin a rehab assignment Tuesday with Single-A Jupiter, Christina De Nicola of MLB.com reports.
Simpson had already been rehabbing at the Marlins' facility in Jupiter, Fla., and after throwing two innings of live batting practice last Wednesday, he's been given the green light to make a one-inning rehab appearance Tuesday. The left-hander has been out since late April while recovering from surgery to address left elbow neuritis and will require multiple rehab appearances before being activated from the 60-day injured list.