Dublin, Waterford and Cork airports in the east had been unaffected.
Ash 'risk' looms
The IAA said a "massive ash cloud" 1,600km long and 1,126km wide remained off the west coast.
"While the northerly winds are keeping the bulk of the cloud out in the Atlantic, the increased size of the cloud continues to pose a risk especially if the winds change," the agency warned.
The shutdown was the third to hit Ireland this week, after two earlier closures led to the cancellation of hundreds of flights and travel misery for thousands of passengers.
The fresh disruption came after Europe's skies were closed for up to a week last month following the eruption of Iceland's Eyjafjallajokul volcano. It was the biggest aerial shutdown in Europe since World War II.
Volcanic ash can cause serious damage to jet engines.
The latest closures triggered the cancellation of hundreds of flights in and out of Ireland and Northern Ireland, bringing fresh chaos to thousands of people.
|Hundreds of flights in and out of Ireland were cancelled due to the latest closures [AFP]
The international airline industry body, IATA, said last month's shutdown had cost airlines about $1.7bn and has called on governments to pick up at least part of the cost.
Eurocontrol, the European air traffic agency, estimates that more than 100,000 flights to, from and within Europe had been cancelled between April 15 and 21 due to the ash.
Iceland's volcano, which is about 1,500km northwest of Ireland, has shown no signs of stopping since it began erupting on April 13.