Francois Louw has come on to the replacement bench for the world champions in place of the Ulster captain, while loose forward Willem Alberts will now cover the locking position should starters Danie Rossouw or Bakkies Botha get injured.
Botha, a surprise inclusion in the side, will enter Saturday's game under a cloud after struggling with an Achilles injury that team management earlier suggested could have ended his World Cup.
Vice-captain Victor Matfield had already been ruled out of the Fiji match after he was replaced in their 17-16 victory over Wales last Sunday with a hamstring strain.
Muller had been hopeful of playing the match at Wellington Regional Stadium just a couple of hours before he was forced to withdraw.
"Everything is all right. We will have a run at the captain's run to see how it goes," he told reporters before he failed the fitness test.
"I don't know whether there's something in the water or what's happening, but no, I think it's just some bad luck we're having at this stage.
"But luckily they're not major, major injuries, they're all sort of a week, 10 days so hopefully we can sort it out quickly."