Zoo officials have yet to confirm the sex of the twins. At least one of the twins is said to weigh just three ounces, which is considered to be premature. A Panda cub is born weighing between 26-200 grams.
"Meimei is such a good mother, taking good care of both of the cubs," zookeeper Tadashi Ishikawa said. "Often, especially in the wild, the mother panda focuses on caring for a healther one and leaves the other one to die."
It was the fifth delivery for the veteran mother, who also gave birth to twin cubs in August 2005 and September 2003.
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.