Jersey Electricity said the storm had caused damage to parts of the island’s network due to fallen trees bringing down overhead power lines.
It said crews had been deployed to assess damage and restore supplies “where it is safe to do so”.
“We recognise how difficult and frustrating it can be to be without electricity and want to reassure customers that we are doing everything possible to restore supplies as quickly and safely as conditions allow.”
Gusts of up to 94mph (151km/h) were reported at Jersey’s airport, which opened two hours later than usual at 07:30 GMT.
Flights arriving and departing from London airports have been cancelled on Friday morning and others delayed – islanders planning on flying have been asked to check directly with their flight provider for travel updates.
Airport operations director Ashley Maggs said there was “limited weather damage” at the airport overnight.