The match with Johnny Gargano planned for NXT TakeOver: New York is effectively off, and it's all but certain that Ciampa will have to vacate the NXT Championship.
Meltzer notes in his report (about 10 minutes into the audio at the above link) that it was known that Ciampa would be out following WrestleMania weekend and that he would try to work through to that point. However, Meltzer speculates that the situation with Ciampa's neck over the past week must have deteriorated to the point where surgery could no longer be delayed.
Stories have emerged over the previous week that Ciampa had been pulled from a handful of outside bookings due to injury reasons.
Meltzer isn't sure the specific nature of Ciampa's injury, but notes that depending on the procedure, recovery time could take between six to 14 months.
As for TakeOver: New York and the Championship, it remains to be seen what new direction NXT will be forced to go into.