It is Tibetan mantra.
In which traditon Om Ma Ni Pad Me Hum mantra is used Mahayana or Thervada?
Or it is used in all three traditions, since this is Buddhism teaching?
It is Tibetan mantra.
The back cover of the book "The Origins of Om Manipadme Hum: A Study of the Karandavyuha Sutra" by Alexander Studholme states:
Om Manipadme Hum, perhaps the most well-known and most widely used of all Buddhist mantras, lies at the heart of the Tibetan system and is cherished by both laymen and lama alike. This book presents a new interpretation of the meaning of Om Manipadme Hum, and includes a detailed, annotated precis of Karandavyuha Sutra, opening up this important work to a wider audience.
The earliest textual source is the Karandavyuha Sutra, which describes both the compassion of Avalokitesvara, the bodhisattva whole power the mantra invokes, and the mythical tale of the search and discovery of the mantra. Through a detailed analysis of this sutra, Studholme explores the historical and doctrinal forces behind the appearance of Om Manipadme Hum in India at around the middle of the first millennium c.e.
He argues that the Karandavyuha Sutra has close affinities to non-Buddhist puranic literature, and that the conception of Avalokitesvara and his six-syllable mantra is influenced by the conception of the Hindu deity Siva and his five-syllable mantra Namah Sivaya. The Karandavyuha Sutra reflects historical situation in which the Buddhist monastic establishment was coming into contact with Buddhist tantric practitioners, themselves influenced by Saivite practitioners.
The mantra "OM mani padme hum" seems to be found only in Tibetan Buddhism.
However, Avalokiteshvara can be found in other non-Tibetan Mahayana traditions like Pure Land Buddhism. Avalokiteshvara is officially not found in the Pali Canon of Theravada Buddhism, even if you can find images of him in some Theravada temples.
Mantras or some kind of phrase for chanting can be found in almost all Buddhist traditions like "namo amitabha buddha" in Pure Land Buddhism, "nam myoho renge kyo" in Nichiren Buddhism and "namo tassa bhagavato arahato samma sambuddhassa" in Theravada Buddhism.
The mantra is not used in Theravāda.
According to this article it is said;
The mantra originated in India; as it moved from India into Tibet, the pronunciation changed because some of the sounds in the Indian Sanskrit language were hard for Tibetans to pronounce.
The mantra Om Mani Padme Hum is found written in two different ways in (and on) Mani wheels and on jewelry, etc.: in the ancient Indian Ranjana script and in Tibetan script.
So it should be belong to either Tibetan Vajrayāna buddhism or Mahāyāna buddhism. One reason I would say so is, Rañjanā script can be mostly found in Mahāyāna and Vajrayāna monasteries.
Usually buddhists in Theravāda school of buddhism don't use mantra.
Note: This is what I understood. I may be wrong but not Dhamma.