One of those killed was a child, and four other people who were in the vehicle have been seriously injured.
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 car rental fell at least six metres (19.6ft) onto the rocky river bank below on its side.
Emergency crews attended the crash site, described as “horrifying” by tour guide Adolf Erlingsson, who was among the first on the scene with two police officers.
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.
Mr Erlingsson said that he can’t understand how the accident happened and had not noticed any ice on the bridge.
“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.
The accident occurred hours before the North Atlantic island saw sunrise, which hit the capital, Reykjavik, at 11.23am.
Johann K Johannsonn, a journalist from Iceland, told Sky News that 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.
It is expected to be replaced in the next few years for a shorter bridge of around 100 metres long, according to information from the Road Administration.
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.
More from World
Donald Trump makes surprise visit to US troops in Iraq
Trump’s trip to Iraq comes amid turmoil at home and abroad
Russia says new missile flies at 27 times the speed of sound and renders all defences useless
Indonesia tsunami: Before and after images reveal dramatic volcano collapse
Indonesia reroutes all flights around erupting Anak Krakatau volcano
Indonesia tsunami: Grim rhythm as search for the missing begins
Last year was the first on record when more foreigners died than residents, according to the Icelandic Transport Authority.