The Newcastle Falcons fly-half missed his club's seventh consecutive Guinness Premiership defeat away to Sale Sharks on Sunday because of concussion.
However, his recent action has been restricted because of a shoulder injury.
The surgery on Wilkinson's injured shoulder, to be carried out at the end of the season, will also rule him out of England's match against the Barbarians at Twickenham on June 1, as well as the two-Test tour.
Rugby Football Union elite rugby director Rob Andrew said: "Of course we would have liked him to tour and we intend to take our strongest available squad.
"But player welfare is important and in this case it is the right call for Jonny not to go to New Zealand.
"We decided with Newcastle Falcons and Jonny that it was in his best interests to have this operation at the end of the season so that he can spend the summer rehabilitating."
Wilkinson became the highest points scorer in Test history during this year's RBS 6 Nations campaign - but lost his place to Danny Cipriani in the final match against Ireland.
However, having signed a new two-year contract with his club, Wilkinson had set his sights on forcing his way back into the team.
He is expected to return for the visit of Worcester Warriors in the European Challenge Cup semi-final.
But once Newcastle's season is over, Wilkinson will undergo surgery on what is described as a "long-standing labral (cartilage) tear".
England play in Auckland on June 14 and a week later in Christchurch. Andrew will oversee the matches, with newly-appointed team manager Martin Johnson staying in England with his pregnant wife Kay.