Under the new measures, people have been told to stay at home and social gatherings are banned.
Some 36 people on the flight from Fiji have tested positive. Four people have caught the virus from community transmission.
Until last week, Kiribati had recorded just two Covid cases.
Kiribati is one of the most isolated islands in the world. It is some 4,800km (2,980 miles) from its nearest continent, Australia.