Police believe she can help explain how the deadly insecticide monocrotophos ended up in the free school lunch.
In all, 47 primary school children fell ill after consuming the meal of rice and soybeans.
The Mid-Day meal scheme, introduced to combat hunger and boost school attendance, provides free food for 120 million children in 1.2 million schools across India.
It often suffers from poor hygiene, and poisoning outbreaks occur from time to time, although rarely if ever with such deadly results.
All of the teachers in Bihar’s state-run primary schools have vowed not to participate in the scheme from Friday.
“Teachers and the headmasters have to manage the scheme with little help, low-quality food and corruption at every level,” said B Sharma, head of the primary school teachers’ association.
“But when such an incident happens, a teacher or the principal is held responsible.”
Earlier, police said scientific tests had detected “very toxic” levels of the pesticide monocrotophos in the deadly meals.
Vegetable oil used to prepare the food was revealed to be highly contaminated.
“It was the high quantity of monocrotophos insecticide found in the food which proved fatal for the schoolchildren,” said Ravindra Kumar, a top police official in Bihar state capital Patna.
The school’s cook, Manju Devi, had earlier accused the school principal, Meena Kumari, of forcing her to use the oil, despite the cook complaining that it “smelled strongly” and looked “dodgy”. She said she was told the oil was “home-made and safe to use”.
State Education Minister, PK Shahi, said it had been bought from the grocery store run by the teacher’s husband.
Police have also been investigating whether the oil was kept in a container previously used to store pesticide.
Reports say Meena Kumari was on her way to the court to hand herself in on Wednesday, but officers stopped her and arrested her before she could go inside.
She faces charges of murder and gross negligence, according to police.
“We have arrested her for questioning,” said Sujeet Kumar, the police chief of Saran district, where the children died.
He told the AFP news agency “we need to talk to her first” before bringing charges.
Bihar Chief Minister Nitish Kumar and other state officials have been criticised for being slow to respond to the tragedy.
“I assure you, those found guilty will be taken to court and punished,” he told a news conference shortly after the arrest.
Locals complained that it took days for any top-level official to visit the village of Dharmasati Gandaman, where the poisoning occurred on 16 July.
There have been widespread protests following the deaths and children across India have reportedly been refusing school meals.