The Karmapa heads one of the four sects of Tibetan Buddhism and could emerge as a future spiritual leader of Tibet on the death of the 75-year-old Dalai Lama, who has said he might not be replaced.
"There should be a thorough investigation. He (the Karmapa) is an important Lama," the Dalai Lama told reporters in Bangalore on Sunday, according to Indian media reports.
"Karmapa has many devotees including from China... some money would have naturally been received by him," added the Nobel prize winner. "There has been some negligence. Better now have a thorough investigation."
The Indian media, quoting unnamed security sources, have reported concerns that the Karmapa could be a Chinese stooge sent to India from Tibet to set up pro-Chinese monasteries.
The office of the Karmapa has dismissed the rumours as baseless and said the money is the result of years of accumulated donations. It has acknowledged negligence in its book-keeping.
Notes totalling $600,000, 1.2 million yuan ($180,000), 500,000 Hong Kong dollars ($64,000), and 5.3 million Indian rupees ($115,000) were discovered at the monastery and other offices, police say.
On Sunday night, about two hundred people held a candlelit vigil in support of the the Karmapa at his Gyuto monastery in Dharamshala, where the Tibetan community in exile is based in India.
The Karmapa fled Tibet in 1999 as a 14-year-old because he said he was concerned that Beijing would force him to turn against the Dalai Lama, who has acted as a father figure for him in Dharamshala.
China regards the Dalai Lama as a dangerous separatist, and has sought to groom monks who would accept Tibet as an integral part of China and drop all claims for an independent state.
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