Leach, who was playing in his first home Test match since the Ashes in 2019, suffered the injury in the sixth over of the match, as he chased a Devon Conway drive to the backward point boundary.
As Leach dived, successfully dragging the ball back from the edge of the rope, he landed heavily on his head, and appeared to injure his neck in the process. New Zealand's medical team were the first on the scene, and attended to him for several minutes before he was able to walk from the field of play back to the pavilion.
However, after subsequent examination from the ECB medical team, the decision was taken to withdraw him from the match.
"Jack Leach has symptoms of concussion following his head injury whilst fielding," read an ECB statement. "As per concussion guidelines, he has been withdrawn from this Test."
In a subsequent statement, the ECB confirmed that he would be out of action for the next seven days at least, meaning his participation in the Trent Bridge Test, which gets underway on June 10, is in doubt.
"Leach will have a graduated return to play with a minimum period being seven days, in accordance with concussion guidelines," the statement added.
Brendon McCullum, England's new Test coach, had made a point of asking players to keep chasing every ball. "Brendon said one basic thing for his mindset is: you chase every ball to the boundary as hard as you can until it's at the boundary edge," Stuart Broad said on Tuesday. "That is just a mindset of positivity, all the time - that you are going to give everything to this game."
Parkinson, who has played nine games for England across the white-ball formats, has been a regular member of touring squads over the last two years and believed he was close to making his Test debut in the Caribbean. He has taken 24 wickets at 25.95 in the County Championship this season, the most of any spinner in the country.
The incident was the only blemish to a remarkable first morning of the Test series for England, who reduced New Zealand to 39 for 6, with James Anderson and Stuart Broad sharing three early wickets before Matthew Potts, on debut, struck three times before lunch.
Andrew Miller is UK editor of ESPNcricinfo. @miller_cricket