"The duchess's condition continues to improve since her stay in hospital last month," the prince's office said in a statement on Monday.
Kate had been hospitalized in London, England, for acute morning sickness early in her pregnancy. She made a rare public appearance last week and appeared to be healthy.
The couple wed in April 2011 at Westminster Abbey.
The child would be third in line to the throne, after Prince Charles and his son, William.
Under an agreement to end gender discrimination reached by the leaders of Britain and 15 Commonwealth nations in October 2011, girls would no longer be placed behind a younger son in the line of succession. Plans are in the works to amend the laws governing line of succession.