Rinpoche, 73, was stabbed along with his nephew and driver at around 11 a.m. Tuesday, the South China Morning Post reported citing a police statement.
According to the statement, police have detained three suspects, who were ethnic Tibetans.
"Following a verbal dispute between the two sides, the three suspects stabbed the three victims to death with knives they were carrying," the statement said.
The Samye Ling monastery Tuesday confirmed that its founder has been killed, the report quoted the monastery as saying.
"Rinpoche's body has been taken to hospital where a post-mortem will be carried out," it said.
Rinpoche was born in 1940 in Tibet's Chamdo prefecture. He was identified as the reincarnation of the abbot of the Drolma Lhakang monastery at a very young age.
Rinpoche fled to India after the Tibetan uprising in 1959. He was the co-founder of the Kagyu Samye Ling Monastery in Scotland.
SRK-Gauri anniversary: B-Town stars and their non-filmi better halves
Birthday special: Popular mothers and daughters in Bollywood
Spotted: 'Kaabil' star Hrithik Roshan with dad Rakesh Roshan
'Rock On 2' trailer launch: Farhan, Shraddha enthrall audience with live gig
Photos: Deepika Padukone, Sushmita Sen with daughters at Mumbai airport