The injury now means England are scrambling to fly out a replacement wicketkeeper, with Ollie Pope likely to deputise initially when the series begins in Christchurch on Thursday.
The incident occurred before the second and final day of England's warm-up match in Queenstown when Cox was receiving throwdowns from assistant coach Jeetan Patel in the nets. Scans confirmed the severity of the break, with the 24-year-old left understandably crestfallen.
"I'm gutted for Jordan," said Brendon McCullum, the head coach. "He has been shaping up nicely, both with the bat and gloves, since we got to New Zealand. That's sport and unfortunately these things happen. We will get around him and look after him. He is resilient and his time will come at some point in the future."
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