Local police said three Tibetans confronted Tarap Shetrup Akong at his home in the southwestern city of Chengdu on Tuesday and killed him, his nephew and his driver after negotiations soured.
Chengdu police say the detained suspects admitted the killings and the case remains under investigation. The British Embassy was not immediately available for comment.
Akong Rinpoche — who was addressed such because of his respected status in the Tibetan Buddhist community — co-founded the Kagyu Samye Ling Monastery in Scotland. He maintained political ties with Beijing and met with a top Chinese leader in 2006 in London.