Chinese police have arrested the head of a kindergarten and her associate over the deaths of two children from a rival school who ate yoghurt injected with rat poison, state media said.

The five- and six-year-old girls from northern Hebei province died after eating the yoghurt which they had found in a bag on the side of the road while walking to school with their grandmother.

The rival kindergarten director Shi Haixia and her associate Yang Wenming "admitted that they injected the poison into the yoghurt and left it on the street", the China Daily said.

"Their intention was to damage the reputation of the rival kindergarten."

The poison contained a strong rat poison called tetramine, the China Daily said, citing a local security official.

The pair were arrested on Wednesday, the same day the younger girl died after a week in hospital. The six-year-old died within hours of drinking the yoghurt on April 24.

The China Daily cited a professor of primary education as saying that the murders exposed the problem of unregulated private schools that had sprung up to compensate for the lack of adequate public kindergartens.

"This is an extreme case showing the lack of supervision in preschool education," it quoted Yuan Ailing of East China Normal University as saying.

Many children in the countryside are cared for by their grandparents because their parents have migrated to cities to find work.