But a second cub was stillborn. Mother Mei Xiang has one other surviving cub, born in 2005.
Pandas are critically endangered and are difficult to breed. A cub born last year in Washington died after six days.
"All the external features looked perfectly normal, so the cub has been described as vibrant, healthy and active," zoo spokeswoman Pamela Baker-Masson told the Associated Press news agency. "This is joyful news."
The baby panda is pink with white fur and has not opened its eyes yet.
Veterinarians took a DNA sample from the cub to establish its paternity.
Mei Xiang had been artificially inseminated with sperm from Tian Tian, the male panda at the same Washington zoo, and a panda from the San Diego Zoo called Gao Gao.
Zoo keepers are expected to try to examine the cub again on Tuesday. Its gender may not be known for two to three weeks.