The England and Wales Cricket Board retained the lineup that secured a five-wicket win at Headingley to take a 1-0 lead in the five-match series.
Archer, who was added to England's test set-up last week for the first time since 2021, missed training on Monday due to a family emergency, British media reports said.
The 30-year-old was called into the squad following England's thrilling five-wicket victory in the opening Test at Headingley last week.
He has not played Test cricket since February 2021 and played his first red-ball match in four years in Sussex's County Championship draw against Durham in Chester-le-Street last week.
Archer is expected to rejoin the squad on Tuesday.
England will look to take a 2-0 series lead over India with victory but the home side have had a mixed bag of results at the Birmingham venue over the last five years.
A defeat by New Zealand in 2021 along with a pair of Ashes losses to Australia in 2019 and 2023 show it could be tough work for England.
ENGLAND XI v INDIA:
Zak Crawley, Ben Duckett, Ollie Pope, Joe Root, Harry Brook, Ben Stokes (capt), Jamie Smith (wk), Chris Woakes, Brydon Carse, Josh Tongue, Shoaib Bashir.
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