Gardaí said the emergency services were first alerted at 12.30am and, a few hours later, Mill Road, Market Street, Townsend Street and parts of Main Street in Skibbereen were flooded.
Sergeant Tony McCarthy said the problems were compounded because the bypass route had been closed.
Extra gardaí were drafted in from Clonakilty to assist while council staff worked to relieve the flooding and remove vehicles abandoned in parts of the town after being caught in three feet of water.
The fire brigade and civil defence rescued a father and daughter from their van as it was caught in the deluge at Mill Road.
Sgt McCarthy said, while some shops and houses were flooded following seven hours of torrential rain, the scene was not as bad as seven weeks ago when the town experienced a tidal flood.
“We are concerned that there could be a freeze again following this, so we are appealing for people not to make unnecessary journeys.”
A number of areas surrounding Skibbereen were also affected; the N71 was closed at Rosscarbery for several hours after a torrent of water carrying rocks and other debris cascaded onto the road from the village.
Gardaí reported that Bauravilla, on the Skibbereen-Bantry Road, was also badly flooded, as were parts of Connonagh and Union Hall.
The national secondary route was also flooded near Innishannon and Leap village, although it was passable. Another black spot, Wolfe Tone Street in Clonakilty, was flooded.
Elsewhere, several homes suffered water damage in Crossbarry while there was also severe flooding between Fivemilebridge and Ballinhassig after streams burst their banks.
In Cork city, Traffic Corps gardaí closed off the Bandon Road, near the Viaduct, for five hours after what was described as “a river of water” flowing onto it around 3am.
Centre Park Road was also closed after it was flooded near Pairc Ui Chaoimh.
ESB crews were also called out as the storm caused electricity outages in several areas, in particular around Macroom.
Met Éireann said two inches of rain fell at its weather station on Sherkin Island.
Freezing temperatures are set to return, however, in the next few days and are expected to continue until January 9.