Youngs has won 20 Test caps, including three for the British and Irish Lions, and featured in all of England’s Six Nations matches earlier this year.
Head coach Stuart Lancaster said: “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. Everyone in the England squad sends them our best wishes.”
Lancaster will also be without prop Alex Corbisiero, back-row Tom Croft and wing Christian Wade, who continue to recuperate from recent injuries.
Wing Jack Nowell underwent a knee operation last week and will also not travel with the squad, while injured pair Billy Twelvetrees and Rob Webber will continue to have respective ankle and knee injuries assessed by England’s medical staff.
The first Test takes place at Eden Park on 7 June.