Most pandas conceived in captivity are the product of artificial insemination but Vienna's Schoenbrunn Zoo said it wanted "to let nature run its course".
Female pandas are only fertile for three or four days each year.
The cub, which measures 10cm (4in) and weighs 100g (0.22lb), is the product of the zoo's two resident giant pandas, female Yang Yang and male Long Hui.
The pair, both now seven years old, were loaned by China to the zoo in Vienna in 2003, and conceived their first cub on 27 April 2007, zoo officials said.
At a news conference, director Dagmar Schratter said the two "live in perfect harmony".
But she said her team "had almost given up", adding that an ultrasound on 6 August had shown no evidence that Yang Yang - whose name means sunshine - was pregnant.
Endangered species
The arrival of the cub was discovered early on Thursday after unusual noises were heard coming from the panda's enclosure. CCTV footage confirmed the birth.
Ms Schratter said the cub, whose sex will not be known for a few weeks, will be named by Chinese officials.
China established a loan system in 1984 under which foreign zoos pay up to £500,000 (740,000 euros; $1m) to house the animals.
The giant panda is native to the upland bamboo forests of China's Sichuan province. However, only about 1,600 remain in the wild, with some 160 in captivity.
Half of the panda's mountainous bamboo habitat was lost between 1974 and 1988 and the animal is listed as endangered on the IUCN Red List of Threatened Species.
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