Jordan, who conceded 97 runs in nine overs during New Zealand's victory in the second game on Friday, has a side strain while Plunkett has a thigh problem, the England and Wales Cricket Board said on Saturday.
A decision on who will replace Plunkett is expected to be made in the next 24 hours.
The series is level at 1-1 after two high-scoring games. The third one-day international is in Southampton on Sunday.
(Reporting by Ed Osmond and Justin Palmer; editing by Sudipto Ganguly)
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