The facility was placed under quarantine last week after authorities confirmed that a 40-year-old asylum-seeker had tested positive for the coronavirus.
Health authorities conducted a total of 2,000 tests in Moria, including 100 on camp staff who tested negative. All 35 migrants who tested positive have been moved to a segregated space and only one has shown COVID-19 symptoms.
Since March 1, all migrants reaching Lesbos have been quarantined away from the island's camps.
The Moria facility, which hosts more than 12,000 people - more than four times its stated capacity - has been frequently criticized by aid groups for poor living conditions.
Most recently, aid groups warned that social distancing and basic hygiene measures are impossible to implement in the camp due to the conditions.
On Monday, Greek authorities said three more migrant facilities had been quarantined: the Eleonas camp in Athens, the Malakasa camp north of the city and the facility in Schisto, near the port of Pireaus.Greece has recently had a surge in COVID-19 infections. On Tuesday, authorities reported 169 new confirmed cases nationwide, bringing the total since the first infection surfaced in February to 11,832 and 290 related deaths.