The England and Wales Cricket Board said in a statement on that Meaker "will return to the England Performance Programme once Finn is available for selection."
Meaker is expected to play in the four-day final warm-up game against Haryana in Ahmedabad from November 8-11.
"Surrey pace bowler Stuart Meaker will join England in India next week, ahead of the four-day game in Ahmedabad, as fast bowling cover while Steven Finn continues his recovery from a thigh strain," the ECB said in a statement.
"The 23-year-old's arrival date is subject to obtaining the necessary visa early next week," it said.
Meaker has featured in two one-day internationals but is yet to make his test debut.
Finn suffered a groin strain in the opening overs of the first game of the tour against India 'A' in Mumbai which ended in a draw. While England are yet to announce the results of the subsequent scans, the call-up of Meaker suggests Finn is unlikely to be fit for the first Test starting in Ahmedabad on November 15.
Graham Onions replaced Finn in the side for the second warm-up game against Mumbai A which began yesterday.
