The crash occurred on Christmas Eve in the town of Zontecomatlan, while the vehicle traveled from Mexico City to the village of Chicontepec.
At this stage we have confirmed nine adults and one child dead," the Zontecomatlan mayor's office said in a statement.
The municipality also released a list of 32 people injured, and the hospitals to which they were admitted.
Fatal road accidents, often involving buses or trucks, are common in Mexico. They are often caused by speeding or mechanical failure.
In late November, 10 people were killed and 20 other injured in a similar accident in the western state of Michoacan.