Centre Crotty and full-back Smith were both forced off in the first half as the All Blacks triumphed 30-15 in the first Test at Eden Park on Saturday.
Damian McKenzie has since been called up as cover for Smith, who suffered another concussion, while Crotty’s likely absence will be covered by Jack Goodhue – a player already with the squad as injury cover.
All Blacks coach Steve Hansen said: “Crotty did a hamstring, right hamstring. He could be two weeks, he could be four weeks, so Jack Goodhue, who’s here, will stay.
“Akira Ioane will [also] stay because Matt Todd has also done a calf during the week in training, so he’s going to go home.”
On Smith’s head injury, Hansen added: “It’s like any concussion. Until such time as he goes through all the protocols and passes them he’s not going to be available.
“It’s day one and he’s still to do anything in regards to testing. It’s not the sort of thing you rush into. We’ll give him a few days.”
Sign up to our mailing list here and we’ll keep you up to the minute with weekly updates from the world of rugby.