Areas around Avoca, Baltinglass, Kiltegan and Rathdrum remain without power following high winds overnight.
The ESB has apologised for the outages.
The company said it hopes to have the service restored to all households by lunchtime today.
Motorists are being advised to use caution while driving this morning.
Motorists should also watch out for wind-blown debris and be particularly mindful of vulnerable road users.