Mahendra Singh Dhoni will captain India in the four-nation limited-overs tournament against Pakistan, Sri Lanka and Bangladesh, in Dambulla from June 15 to 24.
Tendulkar has not played for India since February 24, when he hit an unprecedented double-century in a one-day international against South Africa in Gwalior.
According to the BCCI secretary, Srinivasan, Tendulkar requested the board not to consider him for the Asia Cup as he wanted to spend time with his children.
Meanwhile, Left-hander Yuvraj was dropped after a poor performance in the World T20 cup in the Caribbean.
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