Gusts of up to 130kmph (80mph) were set to batter the west and north west.
Met Eireann warned stormy conditions will develop across the country, with strong gales continuing throughout Tuesday.
Motorists and road users are advised to take extra care as the combination of very strong winds and snow or sleet showers create hazardous driving conditions.
The Road Safety Authority (RSA) said drivers should watch out for falling debris, vehicles veering across the road, and to be extra aware of high-sided vehicles, motorcyclists and cyclists.
"In extreme weather conditions it is best to avoid making a journey by road unless absolutely necessary," the RSA added.
Meanwhile, gardai are investigating the death of a pedestrian who was hit by a truck.
The accident happened on the N20 near Newtwopothouse, Mallow, Co Cork, at approximately 4pm on Monday.
The vicim, a man aged in his late 20s, was pronounced dead at the scene.
His body has been removed to Cork University Hospital for a post-mortem examination.