The 26-year-old sustained the injury in Auckland's NPC and Ranfurly Shield defeat to Canterbury.
Scans in Christchurch after the game cleared the forward of a broken neck, but an MRI scan in Auckland showed a disc prolapse.
In a statement, five-times capped Witcombe said: "Your health is the most valuable asset you can have.
"Injuries are part of the game and you just have to accept them. The support of the medical staff and the team has been great. I will be following their advice closely and will only resume training when I am 100% ready."
Auckland coach Pat Lam said: "Since returning from the All Blacks, Derren's contribution to the team, both on and off the field has been first-class.
"The team and everyone involved in Auckland Rugby will be doing all they can to help him in his recovery."
New Zealand boss Graham Henry added: "We are glad the injury is not as severe as it could have been and we look forward to seeing him back playing whenever this may be."