The supply cut out at around 8.20am. Around 2,000 homes had their power restored within one hour. The remaining homes were reconnected shortly after 10am.
A spokesperson for Northern Ireland Electricity said that a suspected underground network fault is being investigated.
Meanwhile, over 20,000 homes and businesses throughout the region experienced power cuts during the recent severe weather conditions.
A helicopter had to fly emergency teams into the Mourne Mountains on Saturday morning to inspect and restore damaged electricity lines, an incident manager from Northern Ireland Electricity said.
Randal Gilbert added: "We had emergency crews working continuously from Friday lunchtime until Saturday evening to repair all faults on the electricity network. As we repaired faults and restored electricity to some customers, others lost power as a result of the continuing weather conditions.
"At the peak, we had around 4,000 customers without electricity at the same time.
"The snow falls made it very difficult to access the electricity network and to make repairs. Many of the faults were on higher ground or in areas which could not be reached by road due to drifting snow."