The Scarlets hooker will undergo surgery on the problem having had intensive treatment over the past few weeks in the hope of being fit in time.
Wales coach Warren Gatland had admitted that Rees was in "severe pain" in the aftermath of Saturday's 19-9 win over England at the Millennium Stadium and he has been officially replaced in Wales' training squad by Ospreys' Richard Hibbard.
"The safety and longevity of Matthew's career is paramount, we are all very disappointed that Matthew will not be with us at the World Cup but his health is at the fore of our decision," said Wales team doctor Prav Mathema.
"Matthew will not be available for selection after losing his race for fitness from a persistent neck injury. Following a series of injections and intensive treatment and rehabilitation the decision has been made to omit him from the squad to allow him to undergo surgery.
"The medical teams of both the Scarlets and the WRU concluded unanimously to proceed with surgery."
Assistant coach Shaun Edwards gave an indication as to the level of pain Rees was in with the problem, meaning there was no other option than to book the player in for an operation.
"There are more important things in life than rugby and Matthew is in such pain it has to be second to his life," he said.
"We are gutted he will not lead us into the World Cup but he has to take the doctor's advice because you can't live like that. He can't sleep and is in constant agony."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.