The accident happened on the A9 highway near Leipzig about 9.45am, less than two hours after leaving Berlin.
The bus en route to Zurich was operated by Flixbus, the dominant long-distance scheduled bus operator in Germany.
Police spokesman Olaf Hoppe told n-tv television that there were "numerous injured and at least five dead".
Many people were taken to nearby hospitals.
Flixbus said there were 53 passengers and two drivers on board.
The company said it was working closely with local authorities and rescue services.
The cause of the accident was not immediately clear.
Hoppe said there was no indication that any other vehicle was involved.
Police said the driver was not among those killed, German news agency DPA reported.
There was no immediate word on the identity of the victims.
The A9 is a major north-south route that links Berlin with Munich.
The accident happened on a straight stretch of the road just north of a highway interchange at Schkeuditz, next to the Leipzig/Halle airport.
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