Youngs lost his starting place in the England team to Dylan Hartley during this year's Six Nations but played in every game off the bench.
Prop Alex Corbisiero, flanker Tom Croft and wingers Jack Nowell and Christian Wade will not be considered for selection as they continue their recovery from injuries.
"Our thoughts are with Tom and Tiffany at this time and it is entirely right that he stays at home to support her and their daughter Maisie," England coach Stuart Lancaster said in a statement.
"Alex and Tom have worked really hard to come back before the end of the season but they will not have played enough rugby for them to be considered for such a tour. It's the same with Christian Wade."
England play three tests against the world champion All Blacks starting on June 7.
