The rented holiday coach was taking pensioners on an outing to Leipzig to celebrate New Year.
The death toll may go higher, as police and fire brigade officers combed the wreckage.
"We are still clarifying whether there are people under the vehicle," a police spokesman said.
The crash took place on Autobahn 4 in the state of Hesse. According to initial reports, the coach driver swerved to avoid a BMW, lost control of the vehicle, and skidded off the motorway.
It careered through a crash barrier and 50 metres down a wooded embankment.
Photographs from the scene show the coach, with the company name Rexer, resting upright amid trees, but with smashed windows, a crushed roof and debris scattered around.
Five rescue helicopters landed on the motorway to take away the injured. Fire departments from several surrounding areas were involved in the operation. The crash took place on the motorway junction between Kirchheim and Bad Hersfeld.
The crash completely closed the motorway in both directions, and a support centre has been set up, with a telephone hotline. The accident happened at around 10.30am, although the motorway was later partially reopened.
The pensioners were from Baden-Württemburg, and travelling to Leipzig, in former east Germany, according to a spokeswoman of the travel firm.
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