Marsh, 25, a member of the squad which toured the West Indies earlier this year, will replace opener Phil Jaques, who has returned home to seek treatment for a back injury.
"Obviously, I won't be playing but I'll be over there trying my best to get the boys up and doing whatever I can for them," said Marsh, who has played eight one-day internationals for his country.
"It's crazy to be honest with you. It's a dream come true to be on a Test tour.
"It's something I've worked really hard for over the last 12 months."
Chairman of selectors Andrew Hilditch said Marsh was one of the most promising young batsmen in Australian cricket.
"Shaun has been selected having opened the batting for Australia in the one-day international arena and shown great potential," Hilditch said in a statement.
"He has recently moved to opening the batting and played very well in Western Australia's run chase and victory against New South Wales last week.
"As a replacement batsman on the tour, should the opportunity arise, we are confident that Shaun could fill any role in the batting order.
"We have also taken the opportunity to enhance Shaun's international experience as we consider him to be one of the promising young batsmen in Australia capable of having a significant impact in Australian cricket in the future."
The third Test of the four-Test series against India starts next Wednesday (October 29) in Delhi.