Italian media said the portion of highway that collapsed was about 200 yards long.
The Morandi viaduct, completed in 1967, overspans dozens of railway lines as well as an industrial zone housing several factories.
"It was just after 11:30 when we saw lightning strike the bridge", eyewitness Pietro M all'Asa was quoted as saying by Italy's Ansa news agency, reports the BBC. Four people were pulled from the wreckage alive, news outlet ANSA reported.
A man could be heard crying out for God on video at the scene, watching as the bridge collapsed.
The death toll could go higher.
A number of cars and trucks were trapped in the rubble. Other accounts put the death told even higher, and Italy's transportation minister said he expected the final toll would be "an vast tragedy".
Genoa is located between the sea and the mountains of northwestern Italy. In that instance, a truck carrying propane impacted another vehicle stopped in heavy traffic on an overpass, killing one person while injuring over 100.
The Morandi bridge connects the A10 highway which links Italy and France to the A7 highway which runs towards the Italian city of Milan.
Borrelli said highway engineers were checking the safety of the bridge at other points and that some areas were being evacuated as a precaution.
It's still unclear how a torrential rainstorm caused it to fall after having stood for half a century.
Tedeschi said that sniffer dogs are at work in the rubble looking for more injured and victims.
"Operations are ongoing to extract people imprisoned below parts of the bridge and twisted metal", he said. "There will be a time when maintenance costs will exceed those of reconstruction, and then we will have to proceed with the replacement".
About 650 feet of the Morandi Bridge fell onto an industrial section of the port city shortly before noon, according to the Associated Press.
Italy's government Transport Minister Danilo Toninelli said the collapse appeared to be an "immense tragedy".
According to Rai, Italian Prime Minister Giuseppe Conte will travel to Genoa later Tuesday.
French President Emmanuel Macron said on Twitter that France was "by Italy's side in this tragedy and is ready to offer all necessary support".