Thursday will be a day off for Morrison, who will alternate between first base and DH for the Hammerheads this weekend before joining Double-A Jacksonville next week. Morrison, who was 2-for-8 with a walk in his first two rehab games, is recovering from knee surgery in September and has not suited up for Miami since last July.
Marlins manager Mike Redmond would not be surprised to see Morrison return by June 1, assuming the 25-year-old does not have any setbacks.
"I still have never seen this guy play any games," Redmond said. "I've heard a lot about him, and I'm actually, probably just like the fans, I'm really excited to see him play."
Mahoney will alternate between first base and DH through Friday before joining Triple-A New Orleans.
Mahoney was first placed on the 15-day disabled list on March 31 retroactive to March 22 with an intercostal strain. He was recalled from Triple-A on April 17 and played 11 games before landing on the DL again with a right hamstring strain.
Mahoney is batting .276 with a home run and four RBIs for Miami.
Right-hander Nathan Eovaldi (right shoulder) will start for Jupiter on Saturday after throwing a bullpen session Wednesday. Eovaldi will be limited to 60-65 pitches.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter