Two residents in an isles care home and an unconnected patient at the Gilbert Bain Hospital have tested positive for Covid-19.
NHS Shetland says their families have been informed and the patients are being cared for in isolation.
It comes as the health board has learned of other care home residents in different locations who have also begun to display flu-like symptoms.
All those affected have been isolated.
But the health authority has confirmed that the Walls Health Centre has also been closed to face to face patient appointments after a member of staff developed symptoms went into self-isolation.
Patients can still call the surgery for information and advice.
NHS Shetland Chief Executive Michael Dickson said the health authority was facing a “serious situation” but said all those involved were being well cared for.
He added it was imperative that everyone in the isles stayed away from care homes unless they were there to work or provide an essential service.
“This is to protect the people living in these facilities who are among the most vulnerable in our community,” he said.
Mr Dickson said that while the figures of the number of cases of Covid-19 in the isles, issued daily by the Scottish government, had remained static in recent days, the virus was circulating in the isles.
“Do not be lulled into a false sense of security. Wash your hands, maintain social distancing and obey the constraints of the lockdown.
“Our NHS can cope but not with an onslaught of cases,” he said.
Last weekend a patient was airlifted by the RAF from Sumburgh Airport to Aberdeen after he became critically ill with Covid-19.
• NHS Shetland says anyone who has developed a new continuous cough and/or a fever/high temperature should stay at home for seven days from the start of their symptoms, even if they think their symptoms are mild.
People are also being urged to avoid visiting their GP, pharmacy or hospital.
Further advice can be found on the NHS Inform website and patients are asked to phone NHS24 on 111 with Covid-19 related queries.