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.
On Tuesday, the government confirmed that 36 of the 54 passengers had tested positive. It said in a post on Facebook that all passengers are currently being monitored by health officials..
All of the passengers on the flight are fully vaccinated, the government said.
However three members of the quarantine facility's security team have since tested positive. Another person who does not work at the facility has also contracted the virus, the government said.
The lockdown came into force on Saturday but it is not clear how long it will last.
People are not allowed to leave their homes unless for essential services. They can buy essential items from shops but only between 06:00 and 14:00.
"The only way that we can fight this virus is through complete vaccination," the office of President Taneti Maamau said on Facebook. "The public is urged to complete their vaccination doses in order to protect themselves and families."
It is not known what proportion of the 120,000 people in the country have been fully vaccinated.