The group was on a Turkish-flagged freighter which ran aground in Kea's port on Monday during a storm.
Among the refugees, including 38 minors, one person with fever was evacuated to Athens to be tested for the virus, deputy mayor Eleftherios Tzouvaras told AFP.
Three pregnant women and a refugee with a leg injury were also taken to Athens, while three suspected smugglers were arrested, he added.
The rest of the group -- mostly from Afghanistan, Iran and Somalia -- have been quarantined for 14 days in an unused hotel in the island's main port of Korissia, which Tzouvaras said was "not appropriate for refugees".
"Here it's a small touristic island," he said, adding that the group "represents 10 percent of the population, we don't have any infrastructure to welcome them."
A spokesman for Greece's ministry of migration and asylum said that all precautions were being taken to isolate the group, who were receiving care from the Red Cross.
"Several days have already passed since their arrival and they have not been in contact with the local population," the ministry spokesman said.
He added that by Sunday the group will be transferred to "camps like Malakasa" outside of Athens, where dozens of migrants were moved after recently arriving on the island of Lesbos.
The ministry announced on Wednesday new restrictions to the movement of asylum-seekers in island camps to avoid spreading the new coronavirus.
Specialised medical teams were being deployed to the camps and virus isolation areas would be created, authorities said.
There are tens of thousands of asylum seekers in camps on the Greek mainland and islands near Turkey, and most of them are badly overcrowded.