The Health Ministry said the vessel arrived in Lautoka on 2 December to deliver cargo and then proceeded to Suva.
Health Secretary Dr James Fong said the two sailors were under strict quarantine measures.
Twenty-five locals including the local agents of the vessel, staff from Biosecurity Authority, the Ports Authority and Customs were also all in quarantine.
The two sailors had not been classified as Covid-19 border cases yet "because officials are awaiting information on whether they had tested positive for the virus in another country", Fong said.
The information the Health Ministry had so far was that none of the crew left the vessel in Tonga.
The MV Island Chief had arrived in Nuku'alofa from New Zealand, Fong said.
"During that time in New Zealand, the vessel underwent crew change, where individuals were flown in from other countries.
"Our current information is that all crew underwent the 14 days quarantine before the vessel departed.
"The two crew members who were tested positive have been hygienically transferred to Navua Hospital and will be staying at the isolation ward."
The remaining crew members were under quarantine on the vessel under heavy police guard, Fong said.
"No crew member onboard the MV Island Chief had disembarked from the vessel."
Fong said the vessel was next scheduled to depart for Samoa.
In accordance with Samoan entry requirements, the crew underwent a Covid-19 test.
A team from the Health Ministry wearing appropriate personal protective equipment boarded the vessel and collected samples for testing from all 12 crew members, Fong said.
"As a result of this testing, two crew members of the MV Island Chief have tested positive for Covid-19.
"The first sailor tested positive twice on December 4 and 6. The second crew member tested negative on December 4 and then positive on December 6."
Every precaution was being taken to ensure there was no threat to the public, Fong said.
There was also a situation the ministry was taking precautionary measures about in Lautoka and Suva, Fong said, but he did not confirm reports on social media of a suspected lockdown of Lautoka city.
A post had claimed that the Lautoka Port had been quarantined.
Fiji now has 11 active cases of Covid-19, with nine in border quarantine.