Sri Lanka's Muttiah Muralitharan, Chaminda Vaas, Kumar Sangakkara and Lasith Malinga, and Pakistan's Shoaib Akhtar are also unavailable for the three-match series due to either prior commitments or injuries.
Smith, originally named the Africa captain, was replaced by his South Africa team-mate Mark Boucher after undergoing knee surgery last month.
Mahela Jayawardene, who led Sri Lanka to the World Cup final in April, is Asia captain for the one-dayers to be held in Bangalore (June 6) and Chennai (June 9 and 10).
The series, a brainchild of former world cricket chief Jagmohan Dalmiya of India, was launched in 2005 with the aim of raising funds for cricket development in both continents.
But it has yet to catch the public imagination despite being granted official one-day status by the International Cricket Council.
The series was first held in South Africa, but in the off-season due to a crammed international schedule. It was hit by a spate of withdrawals and poor attendances.
It was not played last year due to lack of suitable dates. This time, the series comes immediately after India's tour of Bangladesh and was in danger of being scrapped after original rights holder Nimbus Sports pulled out citing lack of public interest.
It eventually got a lifeline when the pan-Asian ESPN-Star network agreed to broadcast the matches. "The circumstances were such that the tournament could not be cancelled, considering that the matches were designated as official one-dayers," said Asian Cricket Council chief executive Ashraful Haq.
It is no surprise that fans, cricketers and sponsors have shown little interest in the series as it will be played amid a busy schedule and just before the start of a monsoon season in southern India.
Sri Lanka and India are both preparing for serious engagements later this month. Sri Lanka will host Bangladesh while India will tour Ireland and England.
But Asia coach Roger Binny believed the series would still be exciting despite the absence of top players.
"We still have got some big players in both sides," said Binny, a member of India's 1983 World Cup-winning squad.
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