The tragedy took place on Tuesday at the government primary school in Dahrmasati Gandawan village at Mashrakh block, about 25 km from Patna, they said.
The children fell ill soon after eating the meal, which consisted of rice, pulse and soyabean, police said.
They were rushed to Chhapra sadar hospital.
Chief Minister Nitish Kumar has ordered a high level inquiry into the incident, sources in the CMO said, adding that a Forensic Science Laboratory team will assist in the probe, which will be conducted jointly by Saran Divisional Commissioner and DIG.
Kumar also announced a compensation of Rs 2 lakh each to the families of the deceased. Of this, Rs 1.5 lakh is from the Disaster Management Fund and Rs 50,000 from CM's Relief Fund.
Chhapra falls in the Lok Sabha constituency of Rashtriya Janata Dal president Lalu Prasad.
Lok Janshakti Partychief Ramvilas Paswan slammed Bihar Chief Minister Nitish Kumar over death of school students after consuming mid-day meal in Chhapra and demanded his resignation saying these are "not death but murder".
Bihar's opposition RJD has called a bandh in Saran district on Wednesday to protest the death of the students.