Mei Xiang gave birth Sunday at 10:46 p.m., the zoo said. The staff can hear the cub, but has yet to see it because Mei Xiang has built a large nest in her den.
In a news release, Dennis Kelly, the zoo's director, said he was thrilled.
"I'm cautiously optimistic as we haven't seen the cub yet, but we know that Mei is a good mother," Kelly said.
The cub is the second born to Mei Xiang and Tian Tian as the result of artificial insemination. Mei Xiang has had five consecutive pseudopregnancies since 2007 and had a less than a 10 percent chance of being pregnant after so many failed attempts.
Veterinarians will perform the first physical exam after Mei Xiang and the cub have had time to bond, the zoo said. The new mother will most likely not come out of her den, or eat or drink, for at least a week.