He was admitted to hospital earlier this week, the former king’s nephew Tsewang Bista told the AFP news agency.
His health began to deteriorate last year and he suffered from heart and kidney problems.
“He had not been well on and off,” Tsewang Bista said, adding that the former king was “having more difficulty recently because of the cold”.
As a young man, Bista supported a CIA-funded guerrilla campaign to oust Chinese forces from neighbouring Tibet after a failed uprising there in 1959.
The remote Buddhist kingdom of Upper Mustang sits surrounded by canyons on the high, arid Tibetan plateau close to the border with China.