Flashing signs near Avellino, outside Naples, had warned of slowed traffic ahead along a stretch of the A116 autostrada, a major highway crossing southern Italy, before the crash occurred, said highway police and officials, speaking on state radio early on Monday.
They said the bus driver, for reasons not yet determined, appeared to have lost control of his vehicle.
Hours after the crash, fire-fighters said that they had extracted 37 bodies - most of the dead were found inside the mangled bus, which lay on its side , while a few of the victims were pulled out from underneath the wreckage, state radio and the Italian news agency Ansa reported.
The radio report said 11 people were hospitalised with injuries, two of them in very critical condition. It was not immediately known if there were other survivors or any missing.
Rescuers wielding electric saws cut through the twisted metal to better probe the interior of the bus, stopping occasionally in silence to listen for any cries for help, even as the bodies were put into coffins to be taken to a morgue.
Reports said as many as 49 people had been aboard the bus when it ripped through a guardrail after slamming into several cars, then plunged some 30m off the highway and into a ravine near a wooded area.
In its plunge, the bus tore away whole sections of concrete barriers as well as guardrail. The concrete lay in large chunks in a clearing in a wooded area where the bus landed.
State radio quoted Avellino police as saying the bus driver was among the dead.
Occupants of cars which were hit by the bus stood on the highway near their vehicles. One car's rear was completely crumpled, while another was smashed on its side. It was not immediately known if anyone in those cars had been injured.
The highway links western and eastern Italy across the south.
Early reports said the passengers had spent the day in Puglia, an area near the Adriatic on the east coast famed for religious shrines.
But on Monday, a state radio reporter at the scene said authorities told him that the bus had been bringing the passengers home after an outing to a thermal spa area near Benevento, a town not far from Avellino.
Others at the scene said the passengers might have visited a town near Benevento that was the early home of Padre Pio, a late mystic monk highly popular among Catholics in Italy.
Passengers came from small towns near Naples, and relatives streamed to the crash site.
The bus dove off the highway near the town of Monteforte Irpino in Irpinia, a largely agricultural area about 60km inland from Naples and about 250km south of Rome.
A reporter for Naples daily Il Mattino, Giuseppe Crimaldi, told Sky TG24 TV from the scene that some witnesses told him the bus had been going at a "normal" speed on the downhill stretch of the highway when it suddenly veered and started hitting cars.
He said some witnesses thought they heard a noise as if the bus had blown a tire.
A local prosecutor arrived at the crash scene to begin an investigation into the cause of the crash.