The Toyota Land Cruiser was carrying seven Britons when the accident occurred around 9:30 GMT on Thursday (December 27).
The other four passengers were critically injured and airlifted to hospital, Icelandic police have said.
Two of those seriously injured are children aged between seven and nine and the group involved in the crash are from two British families, BBC News reports.
The accident happened in the area of Núpsvötn on Iceland’s ring road between the town of Kirkjubæjarklaustur and area of Skaftafell - part of the Vatnajökull National Park beauty spot.
The 4X4 crashed through a railing on a one-lane bridge, falling around eight metres onto a river bank.
The Foreign and Commonwealth Office said it was supporting the families of those involved in the accident and was in “close contact” with the Icelandic authorities.