Swann suffered discomfort in his bowling arm in last week's tour match against a New Zealand XI and was left out of Wednesday's first Test at the University Oval.
An England and Wales Cricket Board statement later revealed the 33-year-old is to have the operation he has been dreading for much of the past two years.
The hope is that he will be able to recover by early summer and may yet be able to play a part in England's year of back-to-back Ashes.
England are to call up Kent off-spinner James Tredwell for the remainder of the tour, having chosen left-arm orthodox Monty Panesar in this first match of three in Swann's place.
The ECB statement read: "England off-spinner Graeme Swann has been ruled out of the current Test series against New Zealand due to a right elbow injury.
"Swann will travel to the United States next week to have an operation on his right elbow and will then undergo a period of rehabilitation and recovery allowing an anticipated return to competitive cricket in the early summer.
"A further update will be available following the operation."