The 10 children who died in the crash were between the ages of four and 16, the el19digital.com official website said, citing Health Ministry officials, AFP reported.
Some 40 passengers were injured in the accident, it added.
Vice President Rosario Murillo, wife of President Daniel Ortega, said on state-run Channel 4 that around 70 people were crowded on the bus at the time.
She said the accident occurred in Rancho Grande, apparently when the bus driver lost control on a bridge and the vehicle overturned.
“We are deeply moved by this misfortune,“ she said.
Authorities said the bus was speeding, the website said, and police arrested the driver as he tried to flee the scene afterward.
Nine of the victims have been identified so far, Murillo said, without giving their names.
Images in the local press showed the yellow bus impaled by the bridge’s metal railing, while several apparent victims lay on the road nearby.