Bao Bao, the last remaining panda in Germany, was a present from then Chinese communist leader Hua Guofeng to Schmidt during a state visit in November 1980.
The panda lived with its companion Tjen Tjen until her death in 1984 and then was alone in Berlin, despite an unsuccessful attempt to mate him with a female panda called Ming Ming in London in 1991.
During another Chinese state visit, this time by Li Peng in 1994, another panda was promised to the zoo and one year later Yan Yan arrived in Berlin.
Again, all attempts to persuade Yan Yan and Bao Bao to mate proved unsuccessful and the female died in 2007 aged 22.
Bao Bao died "peacefully in his sleep" early in the morning in his enclosure, the zoo said. An autopsy is underway to determine the cause of death.
"Bao Bao will never be forgotten," zoo official Heiner Kloes said in a sombre statement.
China is famed for its "panda diplomacy", using the bears as diplomatic gifts to other countries. About 1,600 remain in the wild in China, with some 300 others in captivity worldwide -- mostly in China.