Statkraft is backing Energy Isles, a consortium of 50 "mainly Shetland-based companies" to develop the project on the remote island.
The consortium has submitted its application to build the project with the Scottish government. If approved, the wind farm could be online by 2026.
The plan is to install 29 turbines with a 200-metre tip height in the north of the island.
Statkraft UK managing director David Flood said the project "fits perfectly with our onshore wind power strategy".
Onshore wind projects on remote islands in the UK, such as Yell, are eligible to bid in to the UK’s contracts for difference support scheme.
In last month’s tender, developers of four wind projects in remote islands totalling 275MW secured support payments.
Uisenis Power won a deal for £39.65/MWh (€44.6/MWh) for its 189MW Muaitheabhal project on the Isle of Lewis, which is due online in 2023/24.
"Over the coming decades onshore wind power has a crucial role to play in helping to meet our climate change targets," said Derek Jamieson, director of Energy Isles.
"As a consortium made up of primarily small to medium-sized local businesses, we were clear from an early stage that there would come a time when we’d need to bring on board the right development partner to help us take things forward," he added.