He said his resignation would make way for other members of the executive team to "grow and realise their full potential", suggesting an internal candidate might be promoted to the top role.
The airline also said it would carry out a global search for a replacement for Fyfe, who gave a commitment to remain chief executive until 2012 when he took over the role in 2005.
Prime Minister John Key yesterday thanked Fyfe for his work with Air New Zealand, and suggested there might be "other opportunities" for the outgoing chief executive - an apparent hint that there might be a role for him in one of the state-owned companies the Government is planning to sell shares in.
Fyfe said the 2008 crash of an Air New Zealand Airbus A320 into the Mediterranean, off the coast of France, was the darkest moment in the almost seven years he spent at the helm. Seven people were killed - five New Zealanders and two Germans.
"There were other moments ... we had an engineer who lost his life at Safe Air [a Blenheim-based subsidiary of Air New Zealand] last year," Fyfe said. "Those moments ... touch you very, very deeply."
He said a significant event came last year, when he travelled to Antarctica with relatives of victims of the 1979 Air New Zealand Erebus disaster.
"To see the impact that had on those people and how that helped them to move forward was one of the more special moments, I think, in my career."
Additional reporting APNZ.