The 21-year-old right-arm seamer joins his twin brother in the squad, Craig Overton having been called up at the weekend when Chris Jordan picked up an injury.
Jordan (side strain) and Plunkett (thigh injury) were ruled out of the remainder of the five-match series following New Zealand???s win in the second match last Friday.
England have earned plaudits for their enterprising play in the series but are trailing 2-1 after the World Cup finalists followed up Friday???s win with a three-wicket success on Sunday.
And the Overton brothers are now both in contention for England debuts, with the remaining matches in the series scheduled for Trent Bridge on Wednesday and Chester-le-Street on Saturday.
Jamie, the younger of the twins by three minutes, was first named in the England squad when he was 19, for the 2013 one-day series against Australia, although he did not play in any of the matches.
Blessed with height (he is six foot, five inches) and impressive pace, he was hampered by injuries and inconsistency last season but has bounced back to produce some promising displays this year and remains a very exciting prospect.
He has a good record in List A cricket, with 20 wickets in 14 matches at an average of 27.