Pietersen has withdrawn for the third and final match at Eden Park after he played the first two Tests of the series.
The 32-year-old was experiencing discomfort in a warm-up match prior to the first Test at University Oval and spent time off the field in Dunedin, where he looked out of sorts while fielding.
He played the second game at the Basin Reserve but the England team management and medical staff decided not to risk aggravating his injury any further in Auckland as Cook's side prepare for back-to-back Ashes series later this year.
"It was done on a game by game basis. Before every game ... you do what you do with every player and assess them before every game," Cook said.
"Clearly he felt, and we felt, he could get through those two games and this game might be a step too far.
"It has got progressively worse so we made the decision that he would now go home and it will be looked at."
Pietersen will return to England later on Thursday to see a surgeon, Cook said, where a full prognosis would be made.
Initial assessments had said Pietersen would need up to six weeks off to recover, suggesting he could be available for the return series against New Zealand before Cook's side host the Champions Trophy one day tournament and then play Australia for the Ashes.
While having a player of Pietersen's calibre, presuming he did not require surgery, well rested ahead of their heavy domestic summer workload, Cook was not over the moon at the prospect of the right hander needing time away from the game.
"At the moment it's not good for English cricket because one of our biggest players and better batters has got injury concerns heading into the English summer. That's not ideal," he said.
"If the injury is not as bad as we hope and it's just a bit of rest needed and no surgery needed then on the plus side he does get some time off and is ready to go for the Ashes.
"But you don't really want time off injured."
Cook's side, like the rest of the series, enter the match at Eden Park as heavy favourites to seal victory. But with the first two Tests badly affected by rain, the match has added significance as the decider - something Pietersen would be sorely missed for.
"Clearly, it's a very important game. To win any series against any nation away from home is a great achievement," Cook added.
"We have got five days of very tough cricket and we want to finish the winter as well as we can (and) you want your best players available.
"He has played through pain the first two games, but he has not been 100 percent fit. There has to be a time when you try and manage the situation as best you can."
Johnny Bairstow would come into the side in place of Pietersen and would bat at six, Cook said. Ian Bell and Joe Root would both move up a spot to accommodate Bairstow.
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