The bus of J S Vidyaniketan was taking the students to school when it met with the accident, police said.
The victims were in the age group of 10-15 years.
Senior police officials have rushed to the spot.
Prime Minister Narendra Modi condoled the death of children in the mishap.
"Anguished by the tragic accident in UP's Etah district. I share the pain of the bereaved families & condole passing away of young children," he said in a tweet.
"I pray that those injured in the accident in Etah recover at the earliest," he said.