Emergency services have said that three children were among the dead, including a baby.
Luigi Brugnaro, Mayor of Venice, described the tragedy on social media as “an apocalyptic scene.”
Upon impact, the battery of the bus, which was an electric vehicle, exploded in flames.
“The scene we found was terrible. It took about one hour to extract some of the bodies,” said Mauro Luongo, commander of the Venice firefighters team.
Onlookers are said to have heard screams coming from the bus after it crashed. However, the fire prevented them from intervening.
The Veneto region governor, Luca Zaia, told state television that the cause of the accident was not clear.
“This is an important tragedy, but it's difficult to understand how it happened," he said.
"The bus was new and electric, and that street wasn't particularly problematic.”
One theory is that the driver, Alberto Rizzotto (41), became ill in the moments before the mysterious crash.
Massimo Fiorese, from La Linea bus company, said it was a new vehicle and Rizzotto was highly experienced.
"There's a video of the bus just before it falls," Fiorese told Ansa news.
"The vehicle arrives, slows down and brakes. It's almost at a standstill when it crashes through the guard-rail. I think the driver must have fallen ill, because otherwise I can't explain it."
There were 39 passengers aboard the bus, which crashed off an elevated flyover before landing near railway tracks. The bus was en route to a campsite near the Marghera district.
Italian prime-minister, Giorgia Meloni has expressed her and the Italian governments deepest condolences to those affected by the accident.
She is said to be in close contact with Mayor of Venice Luigi Brugnaro and Minister of the Interior Matteo Piantedosi and following updates on the tragedy.
