Zoo officials said the cub was found dead Sunday morning after panda keepers heard sounds of distress from its mother, Mei Xiang.
Staffers were able to retrieve the cub about an hour later. The cub appeared to be in good condition, and there were no outward signs of trauma or infection.
"This is devastating for all of us here," National Zoo director Dennis Kelly said Sunday at a news conference. "It's hard to describe how much passion and energy and care has gone into this."
The cub had been a surprise at the zoo. Fourteen-year-old Mei Xiang had five failed pregnancies before giving birth, and only one panda cub has survived at the zoo in the past.
Panda cubs are born about the size of a stick of butter and are delicate infants. Panda mothers are about 1,000 times heavier than their cubs, which are born with their eyes closed. The delicate cubs have died in the past when accidentally crushed by mom. That happened in two different zoos in China in 2009 and 2010 when mothers killed their young while attempting to nurse.
The zoo's first panda couple, Ling Ling and Hsing Hsing, arrived from China in 1972 and had five cubs during the 1980s, but none lived more than a few days. One of the cubs was stillborn, two others died of pneumonia within a day, another died from lack of oxygen after birth, and the final cub died of an infection after four days.
Panda experts have said the first weeks of life are critical for the panda cubs as mothers have to make sure they stay warm and get enough to eat.
"It's kind of a nerve-racking period for the folks that are monitoring mom and cub," Rebecca Snyder, the curator of mammals at Atlanta's zoo, said last week. Atlanta is one of only two other American zoos to have had cubs.
Atlanta has had three cubs, and the San Diego zoo has had six, including a cub born this year. A panda couple in Memphis has yet to have a cub, despite several tries. No other U.S. zoos have pandas.
The cub had not yet been named in accordance with Chinese tradition - it was to receive a name after 100 days on Dec. 24. Had the cub survived until then, it would have been roughly the size of a loaf of bread and weighed around 10 pounds.