Morrison is recovering from right knee surgery, and he opened the season on the 60-day disabled list. Technically, he is eligible to be reinstated on Thursday, but manager Mike Redmond said on Monday that he will need more time.
The 25-year-old first baseman began his rehab stint on May 20, and position players are allowed 20 days on assignment.
Because Morrison has not played in the big leagues since last July, he is striving to get as many at-bat as possible. His assignment ends on June 9, the final day of Miami's road trip at the Mets.
"We want to get him as many at-bats as we can," Redmond said.
Redmond added that Morrison may need the entire stint.
Morrison started off his rehab assignment at Class A Jupiter, where he has played for a week.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter