The children complained of uneasiness after having the mid-day meal at Rasulpur Korigawan primary school near Hajipur in Vaishali district, a district official said.
All the children were admitted to a state-run primary health centre in the district and are said to be out of danger.
"I have asked an official to inquire into it and submit a report soon," the official said.
Police collected samples of the meal, he added. Doctors, who examined the children, did not find any sign of poison.
Last year, 23 students died after eating poisonous meal at a primary school in Saran district.
In Bihar, 16 million students get food under the mid-day meal scheme, which is running in 72,000 schools across the state.