Orn Egilsson, spokesman for Iceland's Civil Defence agency, said flood water had destroyed the 1,233ft long Gigja Bridge as well as a 160ft bridge along the southern coast.
"The flooding is bad. The speed of the water is much more than people imagined," said Mr Egilsson. The flooding is in a remote area and did not threaten human life, he added.
Civil defence authorities were concerned that a third bridge, the 2,950ft long Skeidarar, would also be destroyed by the force of the flooding. "The water is close to one end of the bridge," said Mr Egilsson.
The eruption in the Loki volcano is believed to have begun on 1 October, and a column of steam was observed from the Vatnajokul glacier on the following day. By 12 October, the sub-glacial lake, Grimsvotn, was full to overflowing as a vast pool of melted water built up beneath the ice
Iceland has been preparing for the flooding of the uninhabited black- sand plains at the foot of the Vatnajokul glacier since the eruption.
A reporter with Icelandic National Radio said the flood waters had descended faster than forecast. "In three hours 6,000 cubic metres of water has come down. People can already see ice-blocks on the plains and they expect the bridges to disappear in a few hours," he said.
Emergency services said workers measuring water levels of the many rivers and tributaries crossing the plains had been forced to pull out of the area because of the speed of the torrent, which scientists had previously estimated could surge out at up to 80ft per second. "The water is running extremely fast down on to the sands," said a spokesman for the emergency services in Reykjavik, the Icelandic capital. "There's not so much we can do. We can just watch and wait."
Water was pouring into the ocean along the island's south coast, about 140 miles east of Reykjavik.
The eruption subsided in mid-October but the island has remained on alert for the expected floods, which could wash away the country's coastal ring road, and devastate the power supply system and telecommunication links.
Authorities have been preparing for the torrent by reinforcing dykes and building channels to steer the flood of water, debris and ice-blocks away from vulnerable areas.
The Vatnajokul glacier covers 3,200sq miles and reaches a depth of 3,000ft.