SIC councillors have voted 9-4 to recommend the Scottish government to give consent to Viking Energy's 127-turbine windfarm.
The vote came after a three-and-a-half hour meeting in Lerwick Town Hall on Tuesday morning.
Seven councillors, including three who are directors of Viking Energy, declared an interest and took no part in the meeting. A further two were absent.
A final decision on the project will be taken by the Scottish government's energy minister Jim Mather. An objection from the SIC would have automatically triggered a local public inquiry, but that will now be at the minister's discretion.