Prime Minister Frank Bainimarama confirmed the two cases at a news conference, bringing the national total to seven.
The couple are hairdressers, and their cases are unrelated to the country's five other cases. The pair and their daughter are being isolated at Navua Hospital.
Tracing teams are now trying to locate people who may have come into contact with the family.
The prime minister confirmed that Suva would go into lockdown from 5am on Friday, in a similar fashion to Lautoka, on Viti Levu's west coast, which has been sealed off for two weeks.
Mr Bainimarama said all non-essential businesses will be ordered closed, and people are being asked to stay home.