The destruction of the bridge, just south of the city of Samarra, cuts a vital supply line for the Iraqi army and will further dampen its hopes of retaking the city of Tikrit, further north.
"Daash militants detonated a suicide truck bomb on the bridge over the Tharthar canal, destroying two spans," a police colonel told AFP, using the Arabic acronym for the former name of the Islamic State (IS).
An army source also said the bridge, guarded by army checkpoints at both ends, was destroyed.
Wresting back Tikrit, hometown of executed former president Saddam Hussein, has been one of the government's main objectives since jihadists launched a sweeping offensive in northern Iraq on June 9 and conquered much of the country's Sunni heartland.
Samarra lies 110 kilometres (70 miles) from Baghdad. A mainly Sunni city, it is home to the Askari shrine, one of the holiest sites in Shiite Islam.
Hundreds of volunteers have joined the security forces and Shiite militia in recent weeks to defend the city, which jihadists have vowed to seize.