Tendulkar became the eighth member of the squad to be forced out of the tour through injury and the Indian cricket board has not named any replacement.
"Tendulkar has been ruled out of the series and he will take another four weeks to regain fitness," India team manager Shivlal Yadav told reporters.
Tendulkar missed the first one-dayer at Durham with a swollen toe, ensuring he would not make his eagerly-awaited 100th international century on the tour of England.
Tendulkar, 38, has made 99 centuries in international cricket, 51 in Tests and 48 in one-dayers.
Having scored 274 for seven and reducing England to 27 for two in the first of the five-match one-day internationals at Durham, India looked on course to beat their hosts for the first time on the tour but the match was abandoned due to heavy rains.
Fractured finger
Middle-order batsman Rohit Sharma fractured his right index finger during the match and was ruled out of the series, with Manoj Tiwary called up as his replacement.
Sharma followed Virender Sehwag, Zaheer Khan, Gautam Gambhir, Yuvraj Singh, Ishant Sharma and Harbhajan Singh, who have already returned home with injuries.
The 50-over world champions arrived as the top-ranked Test team but were knocked off their perch as England swept the series 4-0.
The second one-dayer is at the Rose Bowl, Hampshire today.
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