While Elgar and Vilas are also part of South Africa's Test squad for the tour of Bangladesh in July, the A team includes Omphile Ramela, Keshav Maharaj and Dane Paterson, who were rewarded for their good showing in the domestic season.
South Africa A will play a triangular limited-overs series against India A and Australia A. The limited-overs series will be followed by two four-day unofficial Test matches against India A.
"A number of relative newcomers to the Proteas have been included in the South Africa A squads and, with the Proteas due to tour India later this year, this tour will give them invaluable experience of Indian playing conditions," South Africa A coach Vinnie Barnes said.