"He's got a cut on the inside of his right foot at the moment," a New Zealand Cricket spokesman said on Monday.
"He's walking, they don't know too much about the injury at this stage.
"It'll be decided tomorrow as to whether he'll play."
The 22-year-old would miss training at Dunedin's University Oval on Monday, but no other player had been called in as cover, the spokesman added.
Following Dunedin, New Zealand host England in the second Test in Wellington from March 14, with the third and final Test in Auckland starting March 22.