Kate was treated for dehydration related to the ailment in a London hospital for several days last week.
The Sun newspaper said the prince canceled a planned appearance at Sunday night's British Military Tournament at Earl's Court to be with his wife at home.
Kate is scheduled to attend the London premiere of "The Hobbit" Wednesday but sources told The Sun she is unlikely to make it.
William and Kate married in April 2011. They confirmed this month they are expecting their first child. The baby's gender and anticipated birthdate have not been disclosed.