NHS Orkney says it is “profoundly concerned” that Covid-19 is spreading “rapidly” across the islands.
The health board’s chief executive Michael Dickson said several people had developed symptoms and travelled to homes in the isles and the mainland.
The warning comes as NHS Grampian said it was investigating a case of Covid-19 connected to a primary school in Peterhead, Aberdeenshire.
The health board said it was working to establish close contacts.
NHS Orkney has reported no confirmed cases of the virus since 15 June.
But Michael Dickson said he was aware of a “significant number” of positive cases, some of which would be attributed to mainland health board figures.
This happens when a patient’s home address is registered off-island.
It is not known exactly how many people have tested positive for the virus in the islands, or if they are linked to the Aberdeen cluster.
Mr Dickson said: “NHS Orkney is responding to a significant Covid public health issue and we are profoundly concerned that the virus is spreading rapidly across our community.”
He added: “We believe there is a real risk to the people of Orkney, including those on the remote isles, and urge them to take care.
“NHS Orkney is taking this matter extremely seriously and working with partners, which include several NHS mainland boards, port authorities, ferry operators, environmental health and the Orkney Island Council.”
He urged anyone in Orkney who was showing symptoms to self-isolate immediately and seek a test.
A public health team is working to trace the contacts of the positive cases on the islands.
Meanwhile, NHS Grampian has said it is investigating a case of Covid-19 connected to the primary school in Peterhead, Aberdeenshire.
The health board has said it was working to establish close contacts to advise them to self isolate.
Aberdeenshire Council said the reason for closing Peterhead Central on Thursday was a “public health decision”.