Sonny Bill out of Rio Games
The Kiwi team said Williams had been "ruled out with a partial achilles rupture".
"Replaced by Sione Molia," it said in a tweet.
Williams sustained the injury in a tackle during New Zealand's shock 12-14 defeat by Japan in their opening Pool C match at the Deodoro Stadium.
The injury puts into grave doubt Williams's likely availability for the All Blacks' opening Rugby Championship match against Australia on August 20.
Agence France-Presse