The infected passengers were among 73 who arrived in the small Pacific country from Brisbane on Wednesday.
Prime Minister Fiame Naomi Mata'afa also said on Saturday the government may cancel further flights from Australia.
A scheduled flight from New Zealand on Saturday has already been postponed, according to Radio New Zealand.
All the passengers were reportedly fully vaccinated and had tested negative for COVID-19 before departure.
"All positive cases are in isolation sites while the rest of the passengers remain in quarantine facilities," the Samoan government said in a statement on Saturday.
The governor of neighbouring American Samoa, Lemanu Palepoi Sialega "Peleti" Mauga, issued a statement offering words of solidarity to Samoa and support for its prime minister.
He also announced the cancellation of flights between the territory and Samoa for one week.
Samoa, with a population of 200,000, has reported 18 active cases.
American Samoa also has 18 cases, all of them travellers from Hawaii on Hawaiian Airlines flights from Honolulu.
The latest group of seven who tested positive arrived on January 6.
There is no lockdown in American Samoa and flights between Honolulu and Pago Pago continue on limited basis.
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