Link to north
The bridge over a tributary of the Tigris river collapsed on Tuesday when the bomber detonated his explosives-rigged vehicle at a central section, sending three cars plummeting into the water, police said.
Six people were wounded in addition to the fatalities.
The bridge is a key link connecting Baghdad with the town of Taji, around 40km north of Salaheddin province.
Security officials said the blast partially destroyed the concrete structure of the bridge.
"Rescue teams are searching for survivors from the cars which went down after the attack," one official said.
Fighters have regularly targeted Iraqi infrastructure, especially bridges, in an attempt to cut off vital road links between Baghdad and various cities.
Helicopter crash
In other news, a US transport helicopter crashed near an air base west of Baghdad, killing five soldiers, the US military said on Tuesday.
The CH-47 Chinook helicopter was conducting a routine post-maintenance test flight when it went down near Taqaddum air base.
Four US soldiers were reported killed in separate attacks - three in an explosion near their vehicle on Monday in the northwestern Ninawa province.
The fourth died of wounds sustained in combat in western Baghdad.
The deaths raised to at least 3,700 members of the US military who have died since the Iraq war started in March 2003, according to an Associated Press count.
Diyala offensive
The surge in violence comes against the backdrop of a major offensive by US and Iraqi soldiers in Diyala who said it began with a late-night air assault.
Around 16,000 US and Iraqi troops are involved in an operation against alleged al-Qaeda fighters in the province.
Major-General Benjamin Mixon, commander of US troops north of Baghdad, said: "Our main goal with [Operation] Lightning Hammer is to eliminate the terrorist organisations ... and show them that they truly have no safe haven - especially in Diyala."
The operation was described as part of a larger nationwide Operation Phantom Strike, which US forces announced on Monday.
In recent months, US military offensives have taken place near the Tigris and Diyala valleys north of Baghdad and in the Euphrates valley south of the capital.
Civilian deaths
During separate operations by US soldiers in Sadr City, a predominantly Shia area of Baghdad, a local hospital said it had received three bodies, including a five-year-old girl and her father shot dead during the US raid.
Angry mourners marched through the area with flag-draped coffins.
The girl was killed as she and her family slept on the roof of the house to keep cool - a common act for many who live in buildings without air-conditioning.
Lieutenant-Colonel Christopher Garver, a US military spokesman, did not confirm the civilian deaths, and said troops fired only "at people who fired at them".