ESB Networks has said that around 1,500 homes and businesses are without power after strong winds from Storm Diana.
The majority of the outages are in the south west of the country.
Outages had peaked at 11am, with at least 40,000 customers without electricity.
ESB spokesperson Derek Hynes said it was hoped that power would be restored to everyone overnight.
He said where that was not possible, the ESB would be in contact with those customers.
Mr Hynes urged members of the public to take care, saying that falling trees could affect power lines.
A Status Orange weather warning for counties Galway, Clare, Kerry, Cork, Waterford and Wexford has been lifted.
A Status Yellow wind warning for the entire country has also been lifted.
Met Éireann said the strongest gusts during Storm Diana were recorded at Sherkin Island off the West Cork coast at midday, at 122km/h.
Gusts of 115km/h were recorded at Roche's Point in Cork and at Casement Aerodrome, Baldonnel, Co Dublin.
High tide in Cork city this morning passed with only minor spot flooding on the streets.
Tramore (credit Neilus Dennehy) pic.twitter.com/yOjXrH36JN— Damien Tiernan (@damienrte) November 28, 2018