The British royals, currently in Australia, arranged their trip before Meghan's pregnancy was known, sparking fears she and her unborn baby could be vulnerable in the island nations, where Zika is officially listed as a risk.
But WHO said the most recent case of the mosquito-borne virus in Fiji was in 2017 and there had been no recorded cases in Tonga since 2016.
"At the moment, there is really no evidence of a Zika virus outbreak in Fiji," Dr Angela Merianos, a Suva-based communicable diseases specialist with WHO told AFP.
She said the situation was similar in Tonga, adding: "Overall, the risk is low and there lots of things that you can do to decrease that risk even further."
Merianos said all travellers should follow "common sense" precautions to avoid mosquitos, which can carry dengue fever and chikungunya, as well as Zika.
These include wearing insect repellent, using mosquito screens and staying indoors where possible.
"Zika of course is a particular concern for pregnant women and women of reproductive age," she said.
"People should be wearing protective clothing, preferably light coloured, that covers most of the body."
Kensington Palace said after Meghan's pregnancy was publicly announced that the royals had decided to proceed with the trip after seeking advice from doctors about the Zika virus.
Zika normally causes a mild fever that lasts less than a week but if a pregnant woman is infected the baby can develop microcephaly, a smaller than normal head size, and other congenital defects.
Public Health England lists both Fiji and Tonga as moderate risk of Zika.
The British health department's advice for travellers on Fiji states: "Pregnant women should consider postponing non-essential travel until after the pregnancy."
Harry and Meghan will arrive in Fiji next Tuesday, travelling on to Tonga on Thursday.