At least 26 people were killed when the collapse caused cars to plunge almost 150ft, and the death toll is expected to rise further. About 15 people were injured.
Italian premier Giuseppe Conte has visited the city and called the collapse of the 51-year-old bridge "a serious wound for Genoa, Liguria and Italy".
The disaster, on the Morandi Bridge which connects Genoa and other northern cities with beaches in eastern Liguria into France, has focused attention on Italy's ageing infrastructure, particularly its concrete bridges and viaducts built in the post-war boom of the 1950s and 1960s.
What caused the collapse remains unknown, and transport minister Danilo Toninelli has said if negligence played a role "whoever made a mistake must pay".
Early speculation focused on the structural weakness of the span.
Witnesses reported hearing a roar as the 150ft bridge collapsed in torrential rain during midday traffic on the eve of a major holiday that sees most Italians heading for beaches and mountains.
One unidentified woman who was standing below told RAI state TV that it crumbled as if it were a mound of baking flour. Video of the collapse, showing a misty scene of crumbled concrete, captured a man screaming: "Oh, God, oh, God."
Civil protection authorities said at least 30 cars and three heavy vehicles were on the 260ft section of the span that collapsed in the industrial area of warehouses.
There is a huge gap where the bridge used to be, and one heart-stopping image shows a green truck halted on the road just short of the edge.
More than 300 rescue workers and dog search teams are at the scene, using heavy equipment to lift the crumbled concrete and twisted steel.
At least four people have been pulled alive from vehicles under the collapsed bridge.
Angelo Borrelli, the head of Italy's civil protection agency, said: "Operations are ongoing to extract people imprisoned below parts of the bridge and twisted metal."
Officials have evacuated several hundred people living along the raised motorway that traverses the city as a precaution.