Director of Public Health Eretii Timeon told Radio Kiribati they were now waiting for the child's blood test results from Fiji.
In the meantime, his family had been advised to stay home while the baby was receiving treatment.
Mr Timeon said rashes on the child's body, including other symptoms, were slowly disappearing.
A measles taskforce team is closely monitoring the situation.
The ministry said it could not confirm its first case of measles until blood test results return from Fiji.