Legspinner Crane was ruled out of both Tests after the diagnosis of a stress fracture of the lower back.
Leach has received his first senior England call-up and will travel to New Zealand ahead of the two-Test series starting at Eden Park, Auckland on 22 March.
'It's tough for him, ' said England's most successful bowler Jimmy Anderson, who had back problems of his own at the start of his global career.
The 21-year-old, who is a former Thomas A Becket and Lancing College pupil, was named in England's 16-man touring party back in January. "It's tough, especially when you have a chance on a tour like this but it happens unfortunately", he said.More news: Democrat clings to lead in Pennsylvania House race
He will return home and be replaced by left-arm spinner Jack Leach. Crane could only manage 1 wicket in the fifth Test as the Australians sealed the series by winning the final Test.
He underwent remedial work and went on to take 51 wickets in the County Championship in 2017.
At least England had a better day at the start of their second warm-up, taking 13 New Zealand XI wickets or 287 in their 90 overs of batting with Stuart Broad, Moeen Ali and Jimmy Anderson all enjoying productive days.
Leach, 26, was the standout performer on a poor tour for the Lions in West Indies, where they were beaten 3-0 in the four-day matches, with 18 wickets in the three matches convincingly out-bowling Crane.