The 34-year-old loosehead, who was retiring after the tournament, sustained the injury as the reigning champions beat Tonga 47-9 on Saturday to cruise into the quarter-finals as Pool C winners.
The injury will take at least three weeks to heal, so Woodcock's out of the Cup - and rugby.
The third most-capped prop in the history of the game behind Gethin Jenkins of Wales and England's Jason Leonard, Woodcock scored New Zealand's only try in their 2011 World Cup final triumph.
Along with Richie McCaw, Dan Carter and Keven Mealamu, Woodcock was considered a key member of that All Blacks side, and coach Steve Hansen was disappointed his career had ended this way.
"It's not a great way for a great player to play his last test match if he's going to retire," Hansen told reporters. "So it is disappointing for him, but sport's like that, it can be quite cruel."
Woodcock will be replaced in the squad by Crusaders prop Joe Moody, who flew out on Saturday to join the squad in Swansea.
Wyatt Crockett and Ben Franks have also started a match apiece at loosehead prop.
Moody, 27, had been expected to start Canterbury's provincial game against Southland in Christchurch on Saturday but sat in the stands before leaving the ground at half-time.
Canterbury coach Scott Robertson confirmed he spoke with All Blacks manager Darren Shand just after noon on Saturday, and they agreed to let Moody go.
New Zealand will play Ireland or France in the World Cup quarter-finals in Cardiff on Sunday.
A sheep and dairy farmer, Woodcock played for his country at all age levels before making his Test debut against Wales in Cardiff at the age of 22 in 2002.
He soon cemented his place in the New Zealand front row and played all three Tests in the British and Irish Lions triumph of 2005 and four matches at the 2007 World Cup.
Regarded as the best loosehead in the world for his scrummaging and hard work around the pitch, Woodcock's mobility also made him a threat with ball in hand.
He played every match in New Zealand's triumphant 2011 World Cup campaign, 13 Tests in 2012 and 12 in 2013 before injury struck to wreck his 2014 season.
A shoulder injury also ended his 2015 Super Rugby season prematurely and he brought an end to his 12-year career with the Blues in June.
"He's an unsung hero, Woody," Hansen added. "Woody just got better and better and he's been a great player. He's a very mobile footballer and a skilled rugby player.
"He can reflect on his career at some point, when he's ready to do that, with a lot of satisfaction and New Zealanders can be very proud of him."
Woodcock could yet remain in camp, with Hansen saying that's a decision the now-former player needs to make.