Power is expected to be restored to most areas across the county by 6 o clock.
Hundreds of ESB customers have been without electricity since the early hours and could remain without it until this evening.
Gurranbane, Sneem, Kilgarvan and the Loo Bridge areas have all experienced power outages since the arrival of Storm Dennis.
Nationally, 14,000 homes are without power this afternoon.
Gusts of up to 120km per hour are expected while the warning is in place until 10 o clock tonight meaning services in other areas may also be interrupted.
ESB networks is advising customers to ring 1850 372 999 should that happen.