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.
England's unchanged XI means the specialist seamers will once again be Brydon Carse, Josh Tongue and Chris Woakes, the latter playing on his home ground.
Woakes is one of few members of the England team remaining from when Archer made his international bow and told BBC Sport: "He's put in some seriously hard yards to get himself back in condition and a physical state to be at his best.
"He's still relatively young. I believe he's still got his best years ahead of him. That might not be as soon as he gets back but, give him time, and he can certainly be better than he was in 2019."
Harry Brook, left, and Ben Duckett share a joke at training
Bumrah, the best bowler in the world, was outstanding at Headingley, claiming 5-83 in England's first innings.
He has his own history with injuries, including a recent back problem, and India announced before the tour that he will only play in three Tests. After the loss in Leeds, head coach Gautam Gambhir said there would be no deviation from the plan.
Speaking on Monday, former Essex captain Ten Doeschate said: "He's had eight days to recover from the last Test. Given conditions and workload, and how we think we can best manage for the next four games, we haven't made a call on that."
In the hot, dry conditions in Birmingham, Ten Doeschate also admitted a second spinner could join Ravindra Jadeja in the Indian XI.
Left-arm wrist-spinner Kuldeep Yadav, who tormented England on their tour of India last year, is one option, while off-spinner Washington Sundar would add greater depth to the batting line-up.
As England trained on Monday, they were joined by former all-rounder Moeen Ali, who was on hand at his home ground in a coaching role.
