
The coach, heading from Serbia to Poland, crashed at 1:00 am (2300 GMT Saturday) on the M3 highway near Mezokeresztes, east of Budapest, according to a police statement.
The bus, with 57 passengers and two drivers, "left the road, ended up in a ditch, and came to a stop on its side," the national disaster management agency said in a social media post.
Eleven people were declared dead at the scene and another person died in hospital, the agency said. The ambulance service said 37 people suffered minor injuries.
The fire brigade and other rescuers had to drag some people out through the windows because they were trapped in the bus.
It is the worst road accident in Hungary since a train hit a German tourist bus at Siofok in 2003, killing 33 people, reports BSS.
Magyar announced the death toll on social media.
"I send my sincere condolences to the families of the victims," he said. "I thank all the people who took part in the rescue operation."