"Following the latest update from the Met Office, airspace over Northern Ireland will also be closed from 07:00 local time [06:00 GMT on Tuesday]," it said.
The restrictions will close Belfast and Derry airports, it added.
The Irish Aviation Authority (IAA) said it would restrict all flights in and out of Ireland for six hours from 7am on Tuesday (06:00 GMT).
"Ireland falls within the predicted area of ash concentrations that exceed acceptable engine manufacturer tolerance levels," the IAA said.
"The decision is based on the safety risks to crews and passengers as a result of the drift south of the volcanic ash cloud."
The IAA announced later that it would reopen its airspace from 1pm on Tuesday, but warned of further disruption as a result of the cloud.
"Winds are forecast to continue coming from a northerly direction for the next few days and this could lead to further problems,'' it said.
The new alerts should not disrupt aircraft flying over Ireland from Britain or Europe, or southern British airports, including Heathrow, Europe's busiest air hub, air officials in Ireland and Britain said.
Last month airspace across Europe was closed down for up to a week after Eyjafjallajokull erupted, but was re-opened after emergency talks between European governments, airlines and regulators.
The international airline industry body, Iata, said the shutdown cost carriers some $1.7bn.
Eurocontrol, the continent's air traffic control co-ordinator, said more than 100,000 flights to, from and within Europe had been cancelled between April 15 and 21, preventing an estimated 10 million passengers from travelling.