Tendulkar, 35, was expected to be one of the star runners during the Indian leg of the relay here on Thursday, but opted out on the advice of his doctors.
"Sachin has been advised not to take part in the relay as a precautionary measure," the source said. "He has not fully recovered from the groin injury."
Indian Olympic Association chief Suresh Kalmadi said he was unaware the cricketer had pulled out.
"I have just heard these reports, I have not received any communication from him," said Kalmadi.
India's football captain Bhaichung Bhutia had earlier this month withdrawn from the relay in support of Tibetan groups protesting against China's crackdown on their homeland.
Tendulkar did not play in the second and third Tests of the recent home series against South Africa due to the same problem, but hoped to be fit for the Indian Premier League starting on Friday.
Batting maestro needs 172 runs to overtake West Indian Brian Lara as Test cricket's leading run-scorer, a feat he could achieve on the tour of Sri Lanka in July-August.
Tendulkar has 11,782 runs from 147 Tests, second behind Lara's record tally of 11,953 runs.
The prolific Indian is already the top one-day batsman with 16,361 runs and holds the world record of 39 Test and 42 one-day centuries.