Hooker Burns, 27, enjoyed a startling rise to prominence, going from Welsh Premiership club rugby to representing Wales at the World Cup in just 18 months.
But the Newport Gwent Dragons player has now been advised to take a minimum three-month break from the sport.
"Lloyd has been advised to withdraw from rugby for at least three months in order to fully rehab his neck," Dragons rugby director Robert Beale said.
"We are obviously disappointed for Lloyd, particularly with the Six Nations coming up, but Lloyd's safety and welfare has to be paramount."
Burns, Huw Bennett and Ken Owens were Wales' World Cup squad hookers in New Zealand, with Ospreys forward Bennett emerging as first-choice.
Injuries sidelined Matthew Rees and Richard Hibbard from the tournament due to injuries, but they are now playing again and likely to secure berths in Wales coach Warren Gatland's Six Nations squad when it is announced in around 10 days' time.
Burns' Dragons and Wales colleague, lock Luke Charteris, is also set to miss the competition because of injury, while Charteris' second-row colleague Alun-Wyn Jones is recovering from a toe problem that has threatened his participation.
Wales kick off their Six Nations campaign against Ireland in Dublin on February 5.
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