New South Wales batsman Michael Clarke, also uncapped at Test level, will be 28-year-old Hussey's deputy in the three-day match which starts on December 19.
Two of 22-year-old Clarke's rivals for retiring Test captain Steve Waugh's position in the Australia middle order, Queensland's Martin Love and Victoria's Brad Hodge, have also been included in the Australia A team.
"With the Australian side being so successful in recent years, it's difficult for those players on the cusp of selection to break into the national team," chairman of selectors Trevor Hohns said in a statement.
"The side represents a good mix of senior experience and young talent, and reflects our approach of developing players capable of performing at the international
"We've included two young South Australian quicks in Paul Rofe and Shaun Tait for the first time, while young Victorian (one-day team) captain Cameron White will also get his first opportunity at a higher level."
Leg-spinner White and Tait are the youngest players in the side, both aged 20, and Queenslander wicketkeeper Wade Seccombe, 32, is the oldest.
Western Australia fast bowler Matthew Nicholson and Love are the only players in the Australia A side with Test experience.
The December 19-21 match will be India's final preparation for the third Test against Australia starting in Melbourne on December 26.
Australia A: Mike Hussey (captain), Michael Clarke (vice-captain), Chris Rogers, Martin Love, Brad Hodge, Cameron White, Wade Seccombe, Matthew Nicholson, Damien Wright, Paul Rofe, Shaun Tait.