Luke Wright suffered an injury scare during an England training session in Whangarei on Saturday.
England's Twenty20 specialist batsman hurt his right hand in fielding and fitness drills at the Cobham Oval.
A team spokesman confirmed there was no need for any scan after Wright caught his hand on the outfield and took no part in the two hours of batting practice which followed.
Twenty20 captain Stuart Broad is still hoping to be fit in time for Monday's first warm-up match against a New Zealand XI - and Chris Woakes is also desperate to be involved.
"It's great to be here," he said, having played twice in England's 3-2 one-day international series defeat in India last month. "India was good, but this is a new challenge now out here in New Zealand.
"The conditions are different to India, and we need to test them out and get used to them.
"But most of all, we've got to look to win the two warm-up games and get some good momentum going into the actual series."