The Marlins right-hander sustained a fractured right pinky toe on June 29, and the team initially planned on reinstating him on Sunday, his first day eligible to rejoin the team.
Before the Marlins beat the Nationals, 2-1, on Saturday night, manager Ozzie Guillen said: "Right now, we have to make a tough decision, with the front office, with our pitching coach [Randy St. Claire], and figure out what we need the most for the next series to come. We're going to figure out their lineups, and go from there."
But after beating Washington, Guillen said Mujica will throw in another rehab-assignment game at Class A Jupiter on Sunday.
The Marlins recalled lefty Wade LeBlanc when Mujica was placed on the disabled list.
Mujica was injured on a comeback shot off the bat of Philadelphia's Placido Polanco. Recently, he was cleared to see game action, and he threw one inning for Jupiter on Friday.
"It feels good," Mujica said. "I didn't have any plays where I had to run to first, but I ran to the mound, and it felt good."
In 35 games with the Marlins, Mujica is 0-3 with a 4.46 ERA. He's been used mostly in the eighth inning, and he has two saves.