The foundation manager, Piyawut Phetchumpol, said Phlai Boonmee, the male elephant, was recovering from the shock of having his ivory snatched and was being given vitamins hidden inside bananas and pineapples.
Villagers told police believe at least three men arrived on the night of May 4 in a four-door black pickup truck and broke into the foundtion grounds in Hua Hin.
The thieves cut the tusks off Phlai Boonmee and the tail hair off a female elephant also housed there.
It was suspected the theft was ordered by someone for the production of ornaments or auspicious objects for sale.
Similar thefts have occurred twice previously at the foundation and the management has set a 50,000-baht bounty for information leading to the arrest of a culprit.
Police are looking for a mahout who was recently fired for misbehaviour from the elephant foundation. He is identified only as Dok and is a native of Surin province.
In the wake of the theft, Laithongrian Meephan, owner of the Elephant Kraal in Ayutthaya province, said he moved about 30 elephants from a kraal on the bank of the Lop Buri River into the main compound for their protection.
The thieves must be experienced with the use of tranquillisers on elephants, and cutting off the tusks would take only 10 to 15 minutes, Mr Laithongrian said.