"The worst affected areas have been the east coast and midlands. A lot of timber has fallen and the trees have taken down the power lines," the ESB spokesman said.
"We hope to have power restored to most parts of the country by the end of the day."
A Meteorological Office spokeswoman said that wind gusts of up to 78 miles per hour (125 kilometres per hour) had been recorded at the height of the storm.
Police said flooding and fallen trees had blocked roads but there were no reports of injuries.