"The scan results have shown he has a partial stress fracture of the back, we've caught it relatively early so unfortunately, he's going home", Chris Silverwood, England's bowling coach, said on Friday (March 16).
After Crane was ruled out, England bowler James Anderson told the BBC that he believes he will "come back strong" from his injury setback.
After beating the Kiwis in the ODI series 3-1, England is set to take on the hosts in a 2-match Test series which starts on 22nd March. "Around that age you are susceptible to those stress injuries but the advice the lads will be giving him is that he's young, has plenty of time on his hands, is a serious talent and if he works hard I'm sure he'll come back strongly".
The left-arm spinner had been lined-up to join England in India last winter as a replacement for Zafar Ansari until a kink in his action was discovered at Loughborough and he had to have remedial action before returning last summer.
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It is Leach's first senior England call-up.
That followed a chastening Test debut in Sydney when Crane returned the harrowing figures of one for 193 as England collapsed to a 4-0 Ashes defeat.
He had been named in the squad for England's first tour match against a New Zealand XI, which began on Wednesday, but did not play.
He has taken 116 wickets for Somerset in the last two Championship seasons - the most of any Division One spinner - and also impressed on the recent Lions tour.