The zoo said Hua Zui Ba gave birth just before dawn today to a cub weighing 180 grams. The zoo says the cub is "well formed, very active and has excellent vital signs."
It is already suckling, and zoo experts say they are confident of its progress in the crucial first week of life.
The specialists at the Madrid zoo were assisted by experts from China's Chengdu Giant Panda Research Base for Giant Panda Breeding.
They knew the birth was approaching when Hua Zui Ba became increasingly lethargic, stopped eating and began to lick her paws.