Councillors voted 18 to two in favour of a motion to formally explore options “for achieving financial and political self-determination”.
In a debate lasting more than an hour, members argued decision-making has become increasingly centralised and public funding for the islands has been cut under the SNP government at Holyrood.
The motion, signed by council leader Steven Coutts and convener Malcolm Bell, said: “We are concerned that this ongoing situation is seriously threatening the prosperity and even basic sustainability of Shetland as a community.”
Any move for Shetland to become self-determining would need to be supported by an island-wide referendum, councillors stressed.
Mr Coutts suggested devolution has not benefited the area and said the Scottish Parliament feels “remote” to islanders, who face some of the highest rates of fuel poverty in the country.
He added the levels of funding for ferries “negatively impacts on Shetland and everyone of Shetland”, although the Scottish Government said it has provided more than £15 million for ferry services over the last three years.
The Shetland West councillor referenced the 2013 Lerwick declaration by former first minister Alex Salmond, in which he announced plans to decentralise power to Shetland, Orkney, and the Western Isles.
Quoting Mr Salmond, who stated “we believe that the people who live and work in Scotland are best placed to make decisions about our future”, Mr Coutts said: “Replace Scotland with Shetland and that’s the motion here today, and I encourage you to support it”.
After the vote, Mr Coutts welcomed the result and said the council planned to speak to the UK and Scottish Governments next week about options for Shetland’s self-determination.
“The status quo is not working,” he said, adding: “Devolution and the Islands Act have not made any tangible difference to the quality of life.”
Ahead of discussions with the UK and Scottish Governments, Mr Coutts said: “I hope they recognise the challenges of living in Shetland, like the high cost of living, but also the incredible opportunities political and financial self-determination could bring.”
Responding to the vote, islands minister Paul Wheelhouse said neither Shetland nor any other island council had submitted any request for further powers under Additional Powers Request (Scotland) Regulations introduced last year.