Up to 60,000 passengers in Dublin have been affected by the disruption.
Shannon airport authorities say the airport is now closed until at least 8pm this evening, following advice from the Irish Aviation Authority.
Knock airport will not reopen until 7pm. Cork airport remains open, but there are disruptions.
Over 100 flights into and out of Ireland have been cancelled due to the problem, with Aer Lingus cancelling all flights at Irish airports for the rest of the day.
All commercial flights at the City of Derry Airport have been grounded until further notice and George Best Belfast City Airport is also closed.
Further information on how long the disruption is likely to continue is expected at lunchtime.
People intending to travel have been advised to check their airline's website.
The Dublin Airport Authority's Siobhan Moore told RTÉ's Today with Pat Kenny that the event was 'extraordinary'.
UK airspace closed until at least 6pm
No flights will be allowed into British airspace until at least 6pm, the National Air Traffic Services said.
'From midday today until at least 6pm, there will be no flights permitted in UK controlled airspace other than emergency situations,' the air traffic control service said in a statement.
Heathrow and Stansted airports in London suspended all flights at noon because of the volcanic ash cloud which has drifted into British airspace.
In a BBC interview, Britain's National Air Traffic Service Director Paul Haskins said the volcanic eruption is still under way and that the situation is being constantly reviewed.
Ryanair this morning confirmed that it would be unable to operate any services between Ireland, the UK, Norway, Sweden and Denmark or operate flights out of those countries.
The airline says up to 25,000 passengers have been affected by the disruption.
The problems with air travel have resulted in passengers looking to the sea to get to Britain and Europe.
Irish Ferries has reported an increase in bookings and has confirmed there is space on all sailings to the UK and France.
In Scotland, Aberdeen, Edinburgh and Glasgow airports have been closed.
Iceland
The volcano on the Eyjafjallajokull glacier in southern Iceland began erupting just after midnight.
Smoke coming out of the top crater stacked more than 20,000ft into the sky, meteorologists said.
Icelandic public broadcaster RUV reported that a 500-metre fissure appeared at the top of the crater today.
Lava melted the glacier, causing major flooding which forced the evacuation of between 700 and 800 people from their homes in the remote, lightly populated area 125km east of Reykjavík.
'We have two heavy floods coming out from the melting of the Eyjafjallajokull glacier,' police spokesman Roegnvaldur Olafsson told AFP.
'It is very variable how long these eruptions last... Judging from the intensity of this one, it could last a long time,' Magnus Tumi Gudmundsson, a professor of geophysics and civil protection advisor in Iceland, said.
Last month, the first eruption at the Eyjafjallajokull glacier since 1823 briefly forced 600 people from their homes in the same area.
Icelandic airports today remain open as wind blows ash away from the island.