The explosion blew a hole in the steel structure of the bridge spanning the Tigris river in northern Baghdad, police and witnesses told agencies.
Police were seen trying to rescue as many as 20 people whose cars plummeted into the river.
Al-Sarafiya Bridge is one of the oldest and highest in the Iraqi capital.
"We were astonished more when we saw the extent of damage," said Ahmed Abdul-Karim, 45, who also lives near the bridge.
"I was standing in my garden and I saw the smoke and flying debris."
Al-Sarafiyah bridge was built by the British during the 1950s to connect the two sides of Baghdad separated by the Tigris river.
"It is one of Baghdad's monuments. This is really damaging for Iraq. We are losing a lot of our history every day," Abdul-Karim said.
Bus bombed in Kirkuk
In Kirkuk, a mainly Kurdish city in the north of Iraq, a roadside bomb exploded beside a bus, killing six and wounding several others.
Reports said that the bus was taking people to work. Some witnesses said that the workers were travelling either to a local power plant or to oil facilities.
Up to 21 people were said to have been wounded in the attack, the latest indication of rising violence in the oil-rich city which Iraqi Kurds wish to see incorporated into the Kurdistan autonomous region in the north of the country.
Also Thursday, the US military said its troops killed two suspected fighters and captured 17 in raids across Iraq.