"Sachin, while fielding in the Kolkata test, aggravated a knee problem from the ODI series," India captain Anil Kumble told a news conference on Friday.
Kumble, reading a report from physiotherapist John Gloster, said Tendulkar sought a specialist's opinion as soon as he arrived in Bangalore and had been given an injection.
"His condition continues to improve, however, should he have failed to have recover completely in the morning (of the match) we feel it wise to call for a back-up."
Left-handed opener Gautam Gambhir has been called up, Kumble said.
Hosts India lead the series 1-0 after winning the opening test by six wickets in New Delhi. The second test ended in a draw in Kolkata.