The British and Irish Lions flanker's region say it may take Lydiate 12-14 weeks to return from injury.
Ospreys physiotherapist Anthony Carter said Lydiate sustained "a significant injury" to his right shoulder.
Lydiate was injured while leading Wales in their 27-13 pre-tour defeat by England last weekend.
The 28-year-old, who was captaining Wales in the absence of Sam Warburton, has had his place in the Wales squad taken by uncapped Cardiff Blues open-side flanker Ellis Jenkins,
"Dan sustained a significant injury to the AC joint in his right shoulder," said Ospreys senior physiotherapist Anthony Carter, "It was caused by an impact during the England game on Sunday.
"He's been seen by Richard Evans, a shoulder specialist, who confirmed that the shoulder requires stabilisation via surgery, after which there is an expected rehab period of 12-14 weeks."
Lydiate will have surgery this weekend and join fellow Lions Leigh Halfpenny and Alex Cuthbert on missing Wales' summer tour to face the world champions.
Wales' regular skipper Warburton is now over his own shoulder problem ahead of the first of Wales' three Tests against the the All Blacks at Eden Park, Auckland on Saturday, 11 June.
Dan Lydiate could miss the start of the Ospreys' season as he will have surgery on the shoulder injury that ruled him out of Wales' tour to New Zealand.