The condition of another child was stated to be serious, police said.
The children and the woman were taken out from the Parvathi Puthanar canal by local rescuers and rushed to a hospital, where they were declared dead.
According to the driver of the van, the vehicle was carrying nine children and a woman attender of the school.
A search is on to ascertain if any more children were trapped in the muddy bed of the canal.
The children were on their way to their school in Pettah area. All of them were LKG and UKG students.