The bus veered off the road and fell close to railway lines in the district of Mestre, which is connected to Venice by a bridge. The cause of the accident was still unclear.
Sky Italia television reported that 18 bodies had so far been dragged from the wreckage after the vehicle fell 15 metres on to electricity lines and caught fire about 7:45pm on Tuesday (local time).
"It's an apocalyptic scene. I am speechless," Brugnaro posted on X, formerly known as Twitter.
"There are at least 20 dead, but some people are still trapped in the wreckage," he later told Italian state television channel Rai News24.
Italy has had a number of deadly bus crashes in recent years.
In 2017, 16 people on board a bus carrying Hungarian students died in an accident near the northern city of Verona, while in 2013, 40 people died when a bus plunged off a viaduct in southern Italy in one of the country’s worst road accidents.
Venice's prefecture, a branch of the interior ministry, was quoted by Italian news agency ANSA as saying that there were 21 deaths, 12 injured and four or five still unaccounted for.
However, with rescue operations ongoing, other news agencies said the death toll could climb higher.
Prime Minister Giorgia Meloni expressed her condolences, saying in a statement that her government's thoughts were with "the victims, their families and their friends."
