There were 43 passengers aboard and thirteen were injured, three seriously, ten less so, spokesman Tibor Dobson said.
Firefighters are on the scene with blankets and hot beverages to keep people warm in the sub-freezing weather, and a local bus company has dispatched a vehicle to bring survivors into the city of Szeged.
Police spokesperson Anita Lukacs said the bus was carrying guest workers from across the border in Romania.
The three seriously injured passengers and four of the less seriously hurt have been hospitalized in Szeged, she added.
The cause of the accident has not yet been determined.