The bus with 36 children aged between 14 and 15 and five adults on board swerved off the motorway near Kranj, some 30 kilometres (20 miles) north of Ljubljana at 6:00 am (0400 GMT), the Slovenian media reported.
It was one of two buses carrying schoolchildren from Bamberg county in Bavaria to the Croatian island of Krk for an end-of-term trip, according to the internet news site 24ur.
The six injured, including the driver, were kept in hospital, although no one was in critical condition. The remainder of the group are currently in a hotel in Kranj awaiting their return home to Germany.
Police said the cause of accident was not yet clear, but no other vehicle appeared to have been involved.
Most of the children were still sleeping when the accident occurred and not wearing safety belts, according to the Slovenian news agency STA.