The cases were identified on Monday and the ship has been quarantined for at least 14 days.
One of the fishermen who tested positive is i-Kiribati and the other a foreigner.
The i-Kiribati fisherman was returning home after completing a yearlong contract aboard a Taiwanese purse seiner, his last port-of-call before travelling to Kiribati was Papua New Guinea a month ago.
Before reaching Tarawa he transferred from the purse seiner to a carrier vessel or mothership, belonging to the same company, which is the vessel that is now under quarantine off of Tarawa.