Singh handed over the sapling to Thai Prime Minister Yingluck Shinawatra as the 85-year-old King was undergoing treatment in hospital.
The tender sapling will be handed over to the King by Yingluck.
The sapling from the sacred tree reminds of the historic link of the two countries and shared cultural heritage.
"The sapling from the sacred Bodhi Tree, which the people of India are deeply honoured to present as a special gift to His Majesty the King on the occasion of this visit reminds of us our historic links. It also represents the blossoming of our relationship," Singh said in a statement.
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Buddhists revere the holy Bodhi Tree and even the leaves are worshipped by them.
The tender sapling of the tree was flown in on Monday to this predominantly Buddhist nation.
Singh, accompanied by his wife Gursharan Kaur, arrived here today from Tokyo.