Batsman Rohit Sharma will lead the 16-member squad in Kohli's absence during the regional six-team competition to be held from September 15-28.
"Considering the workload, we have given him (Kohli) rest," chairman of selectors M.S.K. Prasad told reporters in Mumbai.
"He has been playing continuously for quite some time. He's on the road since the IPL (Indian Premier League)... we need to preserve some of the precious players, who are playing in all three formats."
Rohit Sharma (c), Shikhar Dhawan (vc), KL Rahul, Ambati Rayudu, Manish Pandey, Kedar Jadhav, MS Dhoni (wk), Dinesh Karthik, Hardik Pandya, Kuldeep Yadav, Yuzvendra Chahal, Axar Patel, Bhuvneshwar Kumar, Jasprit Bumrah, Shardul Thakur, Khaleel Ahmed
Kohli, 29, is currently leading the Indian side in a five-Test series in England where he has scored 486 runs so far including two centuries.
The England series ends on September 11, four days before the start of the Asia Cup.
And in less than a week after the Asia Cup final, India are set to play against the West Indies in a home Test series.
Before the England series, Kohli was forced to miss out on a stint with Surrey due to a neck injury and in the Lord's Test he suffered a lower-back strain.
The selectors also picked 20-year-old uncapped left-arm seamer Khaleel Ahmed who has impressed in the shorter formats of the game.
Middle-order batsmen Ambati Rayudu, Manish Pandey and Kedar Jadhav were brought back after missing India's ODI series against England.
Pacemen Jasprit Bumrah and Bhuvneshwar Kumar were also included with the duo having recovered from their injuries.
Among those who missed out were batsman Suresh Raina and bowler Umesh Yadav.
Sri Lanka, Bangladesh and Afghanistan are the other teams in the fray in the 50-over contest. The sixth team will be decided through a qualifier being held in Malaysia.
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