Morrison underwent offseason surgery on his right knee and has not played with Miami since last July.
Morrison's rehab assignment, which began with Class A Jupiter on May 20, will end in time for him to make his debut on June 9.
However, the Marlins will be playing the Mets in the final contest of a six-game road trip that day, likely pushing back Morrison's return to June 10 against the Brewers at Marlins Park.
The first baseman is currently rehabbing with Double-A Jacksonville.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter