Swedish firm Hexicon AB had already secured approval from Highland councillors for the demonstration project.
The proposed site is about 9km out to sea from Dounreay.
The developer has said that the scheme could generate enough electricity for almost 8,000 homes.
Business, Innovation and Energy Minister Paul Wheelhouse, who approved the project, said: "Once operational, this demonstrator project will help to develop this pioneering technology and cement Scotland's reputation at the forefront of innovation in the renewables sector."
Industry body, Scottish Renewables, has welcomed the government's decision.
Hexicon AB has set up a company called Dounreay TrÃ¬ Limited to develop the wind farm.
The scheme would involve laying a subsea cable and building a substation.
Melvich Community Council has opposed the project because of concerns it would ruin views across to Orkney.
A plan to install two floating wind turbines off the north Caithness coast has been approved by the Scottish government.