Fiji has made measles vaccines free, as it tries to prevent the spread of the disease from New Zealand.
Fiji's Health Ministry said it was closely monitoring the outbreak, which has already moved to Samoa and Tonga.
The ministry is also rolling out training for health workers and urging the public to ensure children are vaccinated before going overseas, especially to New Zealand, Samoa, or Tonga.
"Outbreaks around the world, including in neighboring countries, puts us at risk of having travel related cases of measles," the ministry said in a statement Friday.
However, the ministry said due to an "effective immunisation program in Fiji, measles is rare in the country".
Parents should ensure their children were vaccinated, it said.
In Samoa, an outbreak was declared after a toddler died in Apia's hospital of a suspected measles infection.
Now the virus has reached Tonga too, with its government this week officially declaring a measles outbreak.