Staff said it was only the third successful attempt to breed the endangered species naturally in Europe - the other two cubs also came into the world at the Vienna zoo and are now back in their home country China.
Keepers are keeping their distance to avoid disturbing the mother and child, and still haven't been able to work out its gender.
"Although we are of course very happy, we must remain realistic. The mortality rate for Giant Pandas is around 40 percent during the first year," said zoo director Dagmar Schratter.
Yang Yang and her baby, who was born on Wednesday, will spend the next few months in the breeding box where the birth took place.
The panda house has been closed to the public until further notice.
Giant pandas are one of the world's most endangered species. Their natural home lies in a few mountain ranges in central China. There are about 1,600 known to be living in the wild and some 300 in captivity, mostly in China.
Female pandas are able to conceive only for two or three days in the spring, which makes reproduction difficult. The gestation period is about five months.
Most pandas bred in captivity are conceived through artificial insemination.