NHS Shetland was the only health board in Scotland that did not record a coronavirus case on a day that confirmed cases rose by 806.
Orkney’s total rose by one, and the Western Isles by two, as Shetland remained at 60 confirmed cases for almost a second week.
Councillor Ryan Thomson questioned on social media why the government has “deviated” from local lockdowns.
Mr Thomson said that new data from Public Health Scotland has shown that “Shetland has the lowest infection rate of Covid-19 anywhere in Scotland”.
He said Shetlanders, businesses and the local economy were being “restricted” because of infection rates on the mainland.
“This chaotic, disorderly approach is not working,” he added.
NHS Shetland chief executive Michael Dickson said on Monday it would depend what Shetlanders were “willing to give up” to allow the isles to open restrictions before the rest of the country.