Williams, 31, will miss New Zealand's matches in the Rugby Championship which begins next month after being helped off and taken to hospital in an ambulance during New Zealand's shock 14-12 defeat to Japan in their Pool C opener.
The All Blacks drubbed Kenya 28-5 in their second outing of the tournament without Williams, and face unbeaten Great Britiain at 4pm (BST) on Wednesday needing a win to be sure of progress after GB edged out Japan 21-19 in their second match of the event.
New Zealand Rugby union chief executive Steve Tew said: "He has a partial rupture of his Achilles tendon, which means he will be out of rugby for six to nine months."
Rio 2016
Fiji fans celebrate rugby sevens gold and first Olympic medal
12/08/2016 AT 16:39
World Cup winner Williams - who has excelled in Rugby League and heavyweight boxing - was the biggest name at the Rugby 7s tournament, and gives All Blacks coach Steve Hansen a headache after the retirnament of fellow centre Ma'a Nonu and Conrad Smith after last year's World Cup success in England.
"He's obviously shattered and disappointed," said New Zealand's Olympic coach Gordon Tietjens.
"We've just got to get on with it," said Tietjens.
"The guys bounced back with a lot of character against Kenya."
Rio 2016
Watch Fiji go wild as men's rugby 7s deliver first gold and PM declares public holiday
12/08/2016 AT 07:19
Rio 2016
Fiji thrash Great Britain to take gold - their first Olympic medal
11/08/2016 AT 22:34