Thousands of migrants have been sleeping rough after multiple fires hit the notoriously overcrowded Moria camp last week.
As of Aug. 31, the Moria camp on the island of Lesbos housed 12,714 people, well over its capacity of 2,757.
Officials say the two who tested positive did not display symptoms of COVID-19. Other migrants in the facility and people who come in contact with them are being tested.
While thousands of migrants have been blocked at Turkey's land border with Greece, others have been getting into the country by sea.
Hundreds of protesters on the Greek island of Lesbos on Wednesday threw stones at police who responded with tear gas, stun grenades and rubber bullets
"We are absolutely devastated by this tragedy," MSF wrote on Twitter.