The volcano first erupted underneath the glacier around midnight, causing a 500-meter split in the ice, geologist reported after inspecting the area with helicopters.
There were no reports of human casualties, but authorities evacuated about 500 residents amid fears that the melting ice could cause floods.
All flights have been canceled at the international airport Keflavik and the national airports Reykjavik and Akureyri.
Transatlantic flights have been rerouted to avoid the airspace above the island.
The center of the volcanic eruption had not yet been determined, radio RUV reported.
The island was originally formed by volcanic activity, with numerous volcanic systems continuing to be active in the island's substrata. The most well-known volcano, Hekla, was last atcive 10 years ago.
