Kensington Palace said the couple had been asked to undertake the Scandinavian visit on behalf of the Foreign Office.
The royal household also announced that William is to make a solo official visit to Finland next month.
He will travel to the country, without Kate, on Wednesday November 29 and Thursday 30, also at the request of the Foreign Office.
The Duchess is suffering from hyperemesis gravidarum - a severe form of morning sickness - but made a surprise appearance at a royal engagement on Monday.
She took a twirl with Paddington Bear as they danced on the platform of Paddington Station, watched by William and Prince Harry, at a charity event.
Hidden Sweden: perfect hideaways
Hidden Sweden: perfect hideaways
Most castles and manor houses that have been turned into hotels lose their charm as they chase the corporate market, but you won't find en suite bathrooms, Wi-Fi or TVs in the huge rooms at Kronovall Castle (pictured above). You will find original antiques and wallpaper and, best of all, lashings of lovely bubbles, as the hotel produces its own sparkling wine, Swedish Amadeus. From 1690 SEK (approx £150) per person for a 'summer package', including bed, breakfast, a three-course dinner and sparkling wine tasting. For more information visit petripumpa.se
Head out into the wild and woolly seas of the west coast, to Väderöarna (the Weather Islands), a rocky outpost in the Skagerrak, where you can stay in an old pilot's house and feast on oysters, lobster and prawns fresh from the sea. Overnight stays from 1450 SEK (approx £135) per person, including boat transfers from Fjällbacka, breakfast, lunch and dinner. For more information visit vaderoarna.com
Aficionados of cool, clean Swedish style will be in seventh heaven at Wreta Inn, a 17th century coaching inn deep in the Sörmland countryside. Bedrooms are individually decorated in styles ranging from simple Gustavian to Carl Larsson romanticism. Rooms from 1990 SEK (approx £180). For more information visit wreta.nu
If your dad never quite got round to building that amazing treehouse he always talked about, you can fulfill your childhood dreams staying in this gorgeous cabin built high up in an old oak tree. Sleep surrounded by leaves, sky and stylish Scandie interiors and wake to a breakfast basket winched up to your room. Rooms from 1750 SEK (approx £158). For more information visit Islanna.com
Fans of that wild and wonderful, horse-carrying heroine, Pippi Longstocking, will adore staying at this idyllic wooden cottage in Småland. Not only is it a Villa Villakulla-esque dream, old and wonky and surrounded by a dam and river, its also a short drive from Vimmerby, home to Astrid Lindgren World. Sleeps five. Price from 500 Euros per week. For more information visit sverigestugor.se (cottage no 183)
Forget the Stockholm archipelago, head north and east beyond the Arctic Circle and you'll find a largely undiscovered group of islands scattered out in Bottenviken, halfway to Finland. Stay in a cabin on one of the islands, Kluntarna, and sail, swim and sauna the endless summer nights away. For more information visit lulea.se
Actually, don't forget the Stockholm archipelago - it's stunning, easy to get to from the city and there are enough islands (24,000) for you to be able to find your own secret spot. Utö, one of the larger islands, has a number of cabins to rent. Gather some friends and family for a back-to-nature week staying in Utopia, a comfortable cottage sleeping seven, a short stroll from the sea. Priced at 12000 SEK (approx £1,082) per week in high season. For more information visit utostuga.se
You know that book you've always meant to write? Well, hop on a Ryanair flight to Stockholm Skavsta and high tail it to this idyllic wooden cottage surrounded by forests and lakes. With no Internet, no TV and no phone, if you can't find distraction-free inspiration here, better stick with the day job. Sleeps eight to 10. From £660 per week.
One of the best ways to find a secret corner of Sweden is staying at one of the many farms around the country, which offer bed and breakfast. Try Bockebodagården, a traditional farm in the south of Sweden, where you'll sleep in the old farmhand's cottage and wake surrounded by cows, horses and rolling fields, as well as fresh eggs for breakfast. From 495 SEK (approx £45) per person, per night. For more information visit bopalantgard.se
Åre may be Sweden's biggest and best known ski resort, but to get away from the madding crowds, head to Tänndalen, near the Norwegian border. In winter, ski the miles of silent cross country trails and visit a traditional Sami Market; in summer, spring and autumn, fish, walk, hunt for wild orchids and gorge on cloudberries, which grow only in the far north. Stay in Rökstubben, a 10-bed wooden chalet with sauna, 2km from Tänndalen's alpine area. For more information visit stugvarden.se