The bridge, in Lecco province near Milan, fell when a heavy goods vehicle was crossing, crushing cars below.
The company which runs Italy's main roads has blamed local authorities, saying it had demanded the immediate closure of the bridge hours before Friday's accident.
A preliminary criminal investigation has been opened.
The accident occurred around 17:20 (15:20 GMT) as an articulated lorry carrying a specially authorised heavy weight (108 tonnes) was using the bridge.
At least four other cars were involved in the accident - one was completely crushed underneath the fallen bridge.
Anas, Italy's road authority, insisted it had asked for the bridge to be closed at about 14:00 after one of its workers spotted problems.
It said Lecco province officials had demanded the information in writing - which required a formal inspection of the site. However, the bridge had collapsed before an inspector could reach it.
Lecco authorities have denied Anas's version of events.
One man has been killed and five other people have been injured in Italy after a bridge collapsed over a busy road.