The 26-year-old, who has taken 42 wickets in 13 matches for England in his Test career so far, saw his injury reoccur while playing County Championship cricket for Sussex last week.
England will be starting to sweat over the player's condition ahead of the T20 World Cup in October, followed by the eagerly-anticipated winter Ashes tour of Australia.
England head coach and selector Chris Silverwood is already having to contend with star all-rounder Ben Stokes (broken finger), wicket-keeper Jos Buttler, and bowling trio Chris Woakes, Sam Curran and Moeen Ali all being unavailable for the New Zealand series, and will have some big decisions to make ahead of naming his 16-man squad this week.
Here's a look at the players who could come into the England fold:
He's impressed for Sussex in their handful of County Championship matches so far this season, taking an impressive 29 wickets with an average of 14.
The fast-bowler was named as a reserve in England's last two Test series – Sri Lanka in December, and India in January – and looks highly likely to be involved.
A 6ft 3 bowler capable of bowling over 90mph, Stone is one of England's top rising stars, and he featured in the second Test against India.
He's been in good nick for Warwickshire too, and took 4-89 in a dazzling spell against Essex last month.
Overton hasn’t featured in a Test match for England since the 2019 Ashes series, but is knocking on the door again after impressing with both bat and ball for Somerset.
The current crop:
James Anderson and Stuart Broad both look set to return, after being rotated during the India tour. Mark Wood, who missed the last Ashes series due to injury, should also be selected, but England will be wary of overworking him ahead of a busy winter.
What about spin?
Jack Leach had a tricky time out in India, but will keep his spot. With Ali out, England have been tipped to try out up-and-coming Lancashire star Matt Parkinson, who has been on fire in the County Championship.