There are now 606 cases, up from 337 reported on Sunday.
President Lionel Aingimea said that, as of Wednesday morning, 14 people are in negative air pressure units.
He said the vaccination rate is high, at 98 percent.
This is the first time Nauru has experienced community transmission of the virus.
Just 13 cases had been detected at the borded in late March - they have all since recovered.
Nauru government information officer Kelly Amram said Covid-19 protocols are in place in an effort to slow down the spread of the virus.