Aiden Markram will captain the side, which contains only two frontline spinners in George Linde and Keshav Maharaj, and will rely greatly on pace.
Kagiso Rabada has been included despite missing the last few months with injury, only returning to action in the last week.
Along with Nortje, he forms part of a pace line-up that also includes Marco Jansen, Corbin Bosch, Kwena Maphaka and Lungi Ngidi.
De Kock will likely open the batting after stepping out of retirement late last year, with powerful hitters David Miller, Dewald Brevis and Donovan Ferreira included.
But Stubbs has been left out after a run of indifferent form, while Ryan Rickelton is also dropped.
"We are returning to the subcontinent, where we recently competed against hosts India," coach Shukri Conrad said. "The experience we gained playing in those conditions will undoubtedly benefit us as we head into this tournament.
"Many of the players selected for the World Cup squad were on that trip and experienced first-hand the pitches that we will likely encounter and that will stand them in good stead once we get to India."
South Africa are drawn in Group D alongside Afghanistan, Canada, New Zealand and the United Arab Emirates, and will begin their campaign on February 9th against Canada in Ahmedabad.
South Africa squad
Aiden Markram (captain), Corbin Bosch, Dewald Brevis, Quinton de Kock, Tony de Zorzi, Donovan Ferreira, Marco Jansen, George Linde, Keshav Maharaj, Kwena Maphaka, David Miller, Lungi Ngidi, Anrich Nortje, Kagiso Rabada and Jason Smith.