Witcombe has played against the Lions, South Africa and Australia this year, and has a fearsome reputation.
He was stretchered off after a scrum collapsed on him on Saturday, following an emergency transfer to a local hospital, scans showed that the 26-year-old suffered a slipped disc in his neck.
All Black coach Graham Henry said: "We are glad the injury is not as severe as it could have been."
Auckland team doctor Stephen Kara said the hooker would remain in a hard collar brace for three weeks to see if the bulge in his neck receded.
New Zealand play Wales in Cardiff on 5 November, Ireland in Dublin on 12 November, England at Twickenham on 19 November and Scotland in Edinburgh on 26 November