Moustakas, who singled with two outs in the fourth, scored the Royals' first run on Justin Maxwell's triple off Marlins starter Tom Koehler.
"He felt it starting to get tight rounding second base," Royals manager Ned Yost said. "He came in, scored, went back out and just continued to get tight so he's going to be day to day."
This is the second calf injury in three days for the Royals. Infielder Miguel Tejada sustained a strained right calf on Saturday night and was put on the 15-day disabled list. Moustakas' condition will be reevaluated on Tuesday.
"Tejada's could be some time," Yost said. "I'm hoping that Moose is not, but I can't tell you that right now."
Losing Moustakas would be a huge blow for the Royals. He's been one of the Royals' bright lights in their post-All-Star record of 19-5 with a .293 (24-for-82) average and 13 RBIs since the break. He'd hit just .215 previously.
"He's a pretty tough kid. He's played through a lot of things that nobody really knows about," Yost said and added: "Hopefully thinking, I think he's going to be OK. I think it's just a day-to-day thing."
Moustakas was replaced in the game by Jamey Carroll, just obtained in a trade with the Twins after Tejada's injury. If Moustakas cannot play, Carroll is his likely replacement.