The Karmapa Lama, the third most powerful person in Tibetan Buddhism, is the only person among the religion's senior figures accepted by both the Beijing and the Dalai Lama.
The Karmapa Lama is the only senior Tibetan Buddhist officially recognised by the Chinese authorities and his escape is certain to be an embarrassment.
The 14-year-old Karmapa Lama left his monastry in Tibet's capital, Lhasa, telling guards he was going to a hill-top retreat. He then trekked across the frozen Himalayas to reach Dharamsala, in northern India.
He was accompanied by a small band of monks on the expedition that lasted at least five days.
It is not yet clear whether his intentions are to leave Chinese-ruled Tibet permanently or if it is a temporary measure in order to receive further religious teaching.
After arriving in Dharamsala, he is reported to have met the Dalai Lama, who fled from Tibet using a similar route 40 years ago.
The Karmapa Lama, the third most powerful person in Tibetan Buddhism, is the only person among the religion's senior figures accepted by both the Beijing and the Dalai Lama.
He is said to have evaded his Chinese guards in Tibet by telling them he was going on a religious retreat.
Beijing has issued a statement saying the Karmapa left a letter explaining he was collecting religious artefacts and did not intend to betray the Chinese state.
Correspondents say the statement deliberately avoided criticising the Lama in order to leave the way open for him to return.
But Robert Barnett, a Tibetan expert at Colombia University, New York, said: "It leaves China's religious policy in Tibet in complete disarray."
The BBC has been told that the Karmapa Lama had become increasingly frustrated with a lack of access to religious teachers in Tibet.
He is said to have wanted either permission to travel abroad for lessons from Lamas from his school of Buddhism, or for permission from Beijing for a teacher to visit him.
Chinese recognition
The Karmapa heads the Karma Kagyu - Tibetan Buddhism's second most important, after that headed by the Dalai Lama.
He was the first Tibetan reincarnation to be recognised by the Chinese authorities. He is also accepted as the true reincarnation by the Dalai Lama; a fact that has given him status among Tibet's religious leaders.
In 1992, he agreed to stay in Tibet in return for Chinese recognition. China used the agreement as proof of the legitimacy of its rule in the disputed region.
China considers the Dalai Lama to be an enemy of the state, and there is dispute between him and Beijing over who is the reincarnated Panchen Lama, the religion's second most powerful figure.
Disputed Lama
Last year the Karmapa appeared in public with another controversial reincarnation, the boy who China decided was the Panchen Lama, passing over the Dalai Lama's choice.
Beijing and the Dalai Lama chose their different candidates for the Panchen Lama in 1995.
The Dalai Lama's choice, now 10, and his family have not been seen in public since. Human rights groups believe they are under house arrest.
Beijing's choice was installed by Tibetan monks, surrounded by Chinese officials, in Tashi Lhunpo monastery in Shigatse.
But he is regarded by many Tibetans as a fake