All the children were admitted to a government-run primary health centre and are said to be out of danger.
The children complained of uneasiness after the meal at the Madhmepur middle school in Sursand block, a district official said.
Samples of the meal were collected by police.
The official said some children informed authorities that a "snake-like reptile" was found in the meal.
"It may be true or a rumour. I have asked a district official to inquire into it and submit a report soon," he said.
The doctors who examined the children did not find any sign of poison in their bodies.
A few months ago, a dead rat was found in the mid-day meal served to a student at a primary school in Patna.
In the past, dead lizards, frogs and insects have been found in food cooked in schools in the state.
Last year, 23 students died after eating poisonous meal at a primary school at Dharmasati Gandaman village in Saran district.
A forensic report confirmed the presence of toxic insecticide strains in the cooking oil used for making food at the school.
The mid-day meal scheme is running in 72,000 schools across Bihar, and 16 million students avail of meals cooked under the scheme.