"The birth is expected to take place in March 2012," the Swedish court said in a press release.
The court gave no further information.
Victoria and her husband Prince Daniel, a former gym owner, married last year.
Sweden's monarchy traces its origins back more than 1,000 years, though the current royal family assumed the throne in the early 19th century, when French marshal Jean-Baptiste Bernadotte became King.
He had been elected as successor to the Swedish throne by Sweden's parliament in 1810.
Carl XVI Gustaf has been King of Sweden since 1973. The last Swedish royal wedding was in 1976 when he married German-born Silvia Sommerlath, whom he met at the Munich Olympics in 1972.
Sweden is a constitutional monarchy and the king has no political power, though he is popular in the Nordic country.
The king's popularity has been knocked recently after a book published last year accused him of having an affair among other indiscretions.
Victoria became the heir apparent in 1980 by a constitutional reform that meant that the throne would be inherited by the monarch's eldest child without regard to gender.
(Reporting by Simon Johnson)
Source: Reuters Life! Online Report