However, he said so far nobody had tested positive.
"We are very mindful of the fact that measles is a very infectious disease and that a few cases, in American Samoa will mean that it could easily get across the border," Aiono told RNZ Pacific yesterday evening.
"We're not going to close borders because of it but we will be requiring that anyone travelling to us that they have been vaccinated against measles and that they don't have any symptoms."
Last month, Samoa had suspected cases of measles that came back negative after blood tests were sent to New Zealand.
Aiono said the vaccination rate was too high for another situation like 2019, where a measles outbreak killed 83 people, the majority of them children.
The country is in the middle of a vaccination drive that has been ongoing for about a month.
Aiono said the rate had gone up, in rural areas it is now close to 100 per cent but around the capital the second dose rate was around 40 to 50 per cent.
This handout picture released from UNICEF Samoa shows nurse April Wilson (L) and team leader Luisa Popo preparing vaccinations during a nationwide campaign against measles in the Samoan town of Le'auva'a. Photo: AFP PHOTO / ALLAN STEPHEN / UNICEF