Two other children, aged seven and nine, were among four people seriously injured, police said.
The accident occurred at around 9.30am when the vehicle slammed through a railing while crossing a high single-lane bridge at Skeidararsandur, a vast sand plain in southern Iceland.
The Toyota Land Cruiser rental car fell at least six metres (19.6ft) onto the rocky river bank below, on its side.
While officers doubted the road had been icy, they said humidity could have made the surface slippery.
They are waiting to question the injured, who were airlifted to hospital in Reykjavik.
The Indian Ambassador to Iceland, T Armstrong Changsan, is believed to have visited them.
He told Sky News: “It was quite a horrific scene. The car went off the bridge and just crashed down – I would guess five or six metres – and was really badly damaged.
“When I got there, there were four people out of the car – one of them deceased.
“Three more were trapped inside, two of them probably deceased, and the other trapped under the dashboard.”
Police said it remains unclear what caused the driver to lose control of the vehicle.
It is not known if the seven people in the car were related.
The victims have only been identified as British and their names and ages have not been released.
The Foreign Office is “supporting the family of several British nationals” and is in “close contact with the Icelandic authorities”, a spokesperson said.
“The conditions this morning were not bad at all. The temperature was a little bit above freezing point and I didn’t detect any ice.
“For some reason the driver lost control of the car, hit the railing and plunged down.”
He said he was transporting 19 tourists around south Iceland in his own vehicle, at the time.
The accident occurred hours before the North Atlantic island saw sunrise, which reached the capital, Reykjavik, at 11.23am.
Johann K Johannsonn, a journalist from Iceland, told Sky News the bridge is “really narrow”.
He said the vehicle rolled over in the middle of the bridge and the four people who were seriously injured were rushed to hospital in helicopters.
The bridge over Nupsvotn was built in 1973 and is 420 metres in length.
There have been some accidents on the bridge in recent years, with news site visir most recently reporting a car and van collision in July.
Of the 18 people who have died in traffic accidents in Iceland this year, half of them have been foreign nationals.
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