It's expected it could take several days for the electricity supply to be fully restored to areas served by the Abbeyfeale line.
ESB Networks say this line has been particularly badly affected by Storm Éowyn.
As well as a major fault in the substation, which is preventing power being restored to around 1,200 customers, at least 24 faults have also been found in the line.
The areas affected include Brosna, Mountcollins, Tournafulla and Abbeyfeale.
ESB Networks say their staff and contractors are trying to restore the electricity supply as soon as possible.
To report an outage, call ESB Networks on 1800 372 999.
For updates visit the ESB's Power Check website.