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, 37, 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.
The world’s most prolific Test and one-day batsman turned out for Mumbai Indians in the Indian Premier League in March-April, before being rested for a tri-series in Zimbabwe also featuring Sri Lanka.
“Tendulkar requested the board not to consider him for the Asia Cup as he wanted to spend time with his children in view of the hectic cricket season ahead,” BCCI secretary N. Srinivasan said in a statement.
Left-hander Yuvraj was axed after scoring just 74 runs in five matches in the World Twenty20 in the Caribbean in April-May, where India failed to make the semi-finals.
In five one-day internationals this year, Yuvraj has managed only 96 runs, 74 of them coming in one match against Sri Lanka in Dhaka.
Six players who were rested for the Zimbabwe tri-series — Dhoni, Virender Sehwag, Gautam Gambhir, Harbhajan Singh, Zaheer Khan and Ashish Nehra — are back for the Asia Cup.
The second-string Indian team did not qualify for the final in Zimbabwe after losing twice to the hosts and once to Sri Lanka.
Attacking left-hand batsman Saurabh Tiwary, 20, who plays for Mumbai Indians in the IPL, is the only new face in the squad.
Mahendra Singh Dhoni (captain), Virender Sehwag (vice-captain), Gautam Gambhir, Virat Kohli, Suresh Raina, Rohit Sharma, Ravindra Jadeja, Harbhajan Singh, Praveen Kumar, Zaheer Khan, Ashish Nehra, Pragyan Ojha, Ashok Dinda, Ravichandran Ashwin, Saurabh Tiwary.