Gusts of more than 100mph were recorded on the islands yesterday, forecasters said.
Mainland Scotland also experienced high winds with gusts of 80mph-90mph yesterday.
Scottish Hydro Electric Power Distribution said 5,500 homes in Shetland were without power at the peak of the problem at 3am today, and 1,500 were still off supply at 2.30pm.
It has drafted in engineers from the mainland who are working to restore supplies.
Company spokeswoman Samantha O’Connor said: “We would like to apologise to all of those affected by the interruption to the supplies in Shetland.
“We have drafted in extra engineers to assist with repairs and have successfully restored the majority of homes. We expect the remaining properties to be restored today.”
The high winds also caused difficulties for a coastguard helicopter as it evacuated a female patient from the island of Yell to the main island of Shetland at around 2.30pm yesterday.
The helicopter landed at Sumburgh Airport and the patient was transferred to hospital in Lerwick by ambulance.
Shetland Coastguard said the winds were hurricane force yesterday.
Forecasters said that strong winds might return mid-week.
Daniel Adamson, a forecaster with MeteoGroup, said: “On Wednesday it looks as if we could see gusts as strong as between 70mph and 80mph, mostly in exposed places.”