Manoj Baitha had become a major source of embarrassment for the BJP, which rules Bihar in alliance with Chief Minister Nitish Kumar's Janata Dal United (JDU) as the opposition launched an aggressive political attack over the incident.
Sources say he surrendered after the BJP leadership in the state firmly asked him to do so as the outrage refused to die down.
After his arrest, he was taken to a hospital in Patna to have the injuries he purportedly suffered in the incident treated. He was not taken to a hospital in Muzaffarpur as police feared a confrontation with relatives of the victims admitted there, sources said.
At least nine children were killed and about 20 injured when the BJP leader's speeding Bolero ploughed through them outside a government school building on the outskirts of Muzaffarpur on Saturday. Mr Baitha, who was allegedly behind the wheel, then got off from the car and ran away.
Congress chief Rahul Gandhi on Monday lashed out at Chief Minister Nitish Kumar, a former ally who parted ways to partner the BJP last year, mocking him over his much-publicised prohibition law.
Lalu Yadav's RJD too accused the government of shielding Mr Baitha, threatening huge protests unless he was arrested.
The BJP, which suspended the leader from Sitamarhi on Monday, said he is not an office bearer, as some reports had said.
Bihar Deputy Chief Minister Sushil Kumar Modi said the police were directed to take "sternest possible action" against Mr Baitha irrespective of his political affiliations.