St James's Palace said the Duchess of Cambridge would mark the occasion "privately", and she is understood to be with her husband at their home in north Wales.
Kate was treated last month for a severe form of pregnancy sickness known as hyperemesis gravidarum, whose symptoms include sustained bouts of nausea and vomiting.
The Duchess was admitted to hospital on December 3, a development which prompted the palace to announce that she was in the very early stages of pregnancy.
Health concerns are likely to rule out a celebratory tipple, and rich foods such as pate, oily fish and rare meat are also set to be off the menu.
Kate made her first public appearance since falling ill when she presented cyclist Bradley Wiggins with the main award at the prestigious BBC Sports Personality of the Year awards ceremony in London on December 16 .
The British government is currently pushing through a bill which will end the principle of male primogeniture, meaning William and Kate's first child will succeed to the throne, regardless of gender.
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Three cheers for the Princess!
Is it just me, or does she bear a striking resemblance with Katie Holmes?
BTW, Congratulations your Majesty.