Slade was New Zealand's second-choice fly-half after Dan Carter, but he was ruled out of the rest of the tournament with an injury he sustained during the All Blacks' quarter-final victory over Argentina.
Muliaina injured his shoulder in the same match and announced later that he is retiring from international rugby.
Aaron Cruden, originally called into the squad to cover for Slade when Carter pulled out, now becomes New Zealand's starting fly-half, with Stephen Donald providing cover on the bench.
Hosea Gear narrowly missed out on a place in the original All Blacks selection, but now has the chance to shine as a replacement for Muliaina.
New Zeland face Australia in the semi-finals on Sunday, October 16.