The bus was carrying 44 people when it overturned on a highway near the settlement of Yuzhny, ITAR-Tass reported.
Two of the injured, a 26-year-old woman and a 12-year-old girl, were in "relatively grave condition," said Eduard Kocharov, the director of the regional medical center.
Most of the injured were treated for bruises and cuts from broken glass, he said. Some had broken bones and skull fractures.
Celebrity Families of 2014 [PHOTOS]