Two of the children died Tuesday.
A district health official said: "It is an alarming situation as the disease continue to kill children."
Muzaffarpur civil surgeon Gayan Bhushan said doctors and health experts were eagerly awaiting the onset of monsoon as the rains are likely to slowdown the spread of the disease.
Monsoon is likely to enter Bihar June 11 or 12.
Over a dozen children were warded in government hospitals and private nursing homes in Muzaffarpur, about 70 km from here.
The symptoms of this mosquito-borne disease include high fever, irritation and swelling in the brain.