The mishap happened on the Mandya Keregodu main road, near Sathanur, about seven kms from here, officials said.
There were 45 passengers in the bus when the accident happened, officials said adding "those injured included many children who were returning from schools."
The injured have been shifted to Mandya Institute of Medical Sciences where the condition of eight persons was stated to be critical.
"Driver of the bus was trying to overtake a private bus that is when he noticed another bus coming in the opposite direction. When he applied brakes, the bus swerved to the right and broke through the parapet wall," officials said.