Sixty-three percent of those surveyed by the Aftonbladet newspaper said they would like to see the king make way for the 33-year-old princess within the next 10 years. Only 30 percent said he should reign until his death, while the remaining seven percent did not offer an opinion.
The poll comes after the recent publication of a tell-all biography of the king which included details of his affairs with a string of younger women, including Camilla Henemark, lead singer with pop group Army of Lovers.
Other members of the Swedish royal family have also found themselves the target of lurid tabloid reporting in recent months, including Prince Carl Philip who has been romantically linked to a reality TV star.
Princess Madeleine, the younger daughter of King Carl and Queen Silvia, broke off her engagement with her long-time boyfriend in April after it emerged that her fiancée had had an affair with a Norwegian handball player.
Her older sister Victoria, who married her former fitness instructor in the summer, is the most popular member of the royal family, according to the poll.
The monarchy as an institution, however, remains popular with 74 percent of those surveyed supporting its continuation.