Tendulkar has been carrying this injury for quite a while but the problem aggravated before the opener of the five-match series.
"Tendulkar has been ruled out of the series and he will take another four weeks to regain fitness," team manager Shivlal Yadav said.
The veteran batsman, who captains Mumbai Indians, is also almost certain to miss the Champions League Twenty20 event to be held at four venues in the country from September 19 to October 9.
The batting maestro, who is just one short of completing the incredible milestone of 100 international centuries, will have to wait longer with this latest injury.
The team is already missing key players such as Virender Sehwag, Gautam Gambhir, Yuvraj Singh, Rohit Sharma, Ishant Sharma and Zaheer Khan due to injuries.
Tamil Nadu batter Subramanium Badrinath has been called up to replace Sachin Tendulkar.
