The baby pandas were born on Saturday at Adventure World in Wakayama, 280 miles southwest of Tokyo. Officials have yet to confirm their sex, spokesman Tadashi Ishikawa said.
Although one of the twins weighs just three ounces, considered to be premature, both babies and Mei Mei were in good health, Ishikawa said.
Mei Mei, 12, and partner Eimei, 14, are both on loan from China.
China's Xinhua News Agency said that their birth raised the number of artificially bred pandas born this year to a record 30.
Ishikawa said, however, that officials could not confirm if the twins were born as a result of natural mating or artificial insemination because both methods were tried on the couple.
The panda is one of the world's rarest animals, with about 1,590 living in the wild in China, mostly in Sichuan and the western province of Shaanxi. Another 180 have been bred in captivity.