The accident yesterday in Malam Sidi village in Gombe state was due to a brake failure, said police spokesman Ahmed Usman.
"A total of 11 children died in the incident while 17 others were seriously injured," Usman told AFP.
He said the victims were aged between 11 and 15, prompting an angry mob to descend on the bus driver and beat him to death.
Police have launched an investigation into the accident, he added.
Nigeria is almost evenly divided between a mainly-Muslim north and predominantly Christian south.