Archer, who burst onto the international scene in 2019, has not played a Test since 2021 after a string of back and elbow injuries.
He has been carefully nursed back to fitness on a diet of white-ball cricket and played for Sussex in the County Championship last week, taking one wicket in 18 overs.
Both former England captain Michael Vaughan and Sussex coach Paul Farbrace, also a former England assistant coach, urged caution with rushing Archer back to the Test arena after such limited first-class bowling.
England had the option of releasing Archer to play in the final two days of Sussex’s Championship match against Warwickshire, on Tuesday and Wednesday, but he will remain with the national team.
All of the other members of the squad who are not playing in the second Test – Jacob Bethell, Sam Cook and Jamie Overton – will also stay in Birmingham. There is a short turnaround to the beginning of the third Test at Lord’s, starting on 10 July.