The news drew congratulations from around the world, with the hashtag "royalbaby" trending globally on Twitter.
The couple's first child will be third in line to the throne -- behind William and his father, Prince Charles -- leapfrogging the gregarious Prince Harry and possibly setting up the first scenario in which a female heir could benefit from new gender rules about succession.
The palace would not say how far along the 30-year-old duchess is, only that she has not yet reached the 12-week mark.
Palace officials said the duchess was hospitalized with hyperemesis gravidarum, a severe form of morning sickness that affects about 1 in 200 women and can lead to dehydration or worse if left untreated. They said she was expected to remain hospitalized for several days and would require a period of rest afterward.