Shaw had captained the India U-19 side during the limited overs series on the England tour in August.
"The selectors were of the opinion that 17-year-old Prithvi Shaw, who recently scored a century (154) in the Duleep Trophy final, should play in the ongoing Ranji Trophy," said the BCCI in a statement.
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A BCCI official, who did not wish to be quoted, said the decision was taken in consultation with India A and U-19 coach Rahul Dravid, who wants the rising Mumbai batsman to focus more on Ranji Trophy.
Shaw, who hit a hundred on First-Class debut in last year's Ranji final between Mumbai and Tamil Nadu, also struck a match-winning century in the Duleep Trophy final last month.
Himanshu Rana will captain the U-19 squad in Shaw's absence. The Asia Cup will be held in Malaysia from November 9-20.
The tournament was supposed to take place in India but Pakistan objected to travelling to the neighbouring country, citing security concerns.
The Squad:
Himanshu Rana (Captain), Abhishek Sharma (vice-captain), Atharva Taide, Manjot Kalra, Salman Khan, Anuj Rawat, Harvik Desai, Riyan Parag, Anukul Roy, Shiva Singh, Tanush Kotian, Darshan Nalkande, Vivekanand Tiwary, Aditya Thakare, Mandeep Singh.