Both countries are listed as "moderate" risk.
The NHS advises that infection with the virus during pregnancy "can lead to congenital Zika syndrome, with severe consequences for the baby".
"If you plan to travel to an affected area, seek travel health advice before your trip," it continues.
"It is recommended that pregnant women should consider postponing non-essential travel to areas at moderate risk of Zika virus transmission until after pregnancy."
Sources said that the Duchess has been taking advice on all medical issues, with the couple making the decision to go ahead with the tour after taking it into consideration.
The inclusion of Fiji and Tonga in the itinerary had previously been cited by royal-watchers as a sign that the duke and duchess could not be expecting a baby just yet.
The couple is, Kensington Palace said, "delighted" with the news.
The announcement, ahead of the first day of their 16-day tour, will add an extra pressure to an already busy tour.
The schedule is currently weighted towards the morning and early afternoon, with most evenings kept free of engagements.
The Duchess is currently absent from just one: a wreath laying at a war memorial first thing in the morning in Suva, Fiji, where her husband will go alone.
It is understood that the duchess plans to attend every other event as detailed in her public schedule, but will necessarily see how she feels as the gruelling tour continues.
The Zika infection is spread by the Aedes species of mosquitoes, which tends to bite during the day.
It usually causes mild symptoms of fever, headache, muscle pain and a rash, but can have severe complications for unborn children.
Zika virus | Quick facts
• The Zika virus was first identified in Uganda in 1947
• It is transmitted through the bite of an infected Aedes aegypti and Aedes albopictus mosquito
• The link between the virus and birth defects was only identified when there was an outbreak of the disease in South America in 2015 and 2016
• More than 3,000 babies have been born with birth defects linked to the virus
• Scientists have yet to work out exactly why the virus causes birth defects