Fierce winds uprooted trees and electric poles and caused widespread damage in three districts.
Five other districts near the Kosi river were also affected, a disaster management official said.
Reports said several dozen people were injured and the toll was expected to increase.
The storm hit the districts of Purnea, Saharsa, Madhubani, Darbhanga, Katihar, Kishanganj, Supaul and Madhepura.
Thousands of huts, housing impoverished labourers, were destroyed, along with crops of wheat, maize, and pulses, the Press Trust of India reported.
The principal secretary of Bihar's disaster management department, Vyashji Mishra, said "communication and electricity have been disrupted and roads are blocked with uprooted trees".
He said the extent of the damage would become clearer after all affected areas had been accessed.
Bihar's director general of police, PK Thakur, said rescue workers were still trying to reach some of the storm-hit areas, the AFP news agency reported.
Schoolteacher Alok Anand, in the worst-affected Purnea district, wrote on Facebook that the storm was "like a hurricane".
"Many homes have been destroyed and many people have become homeless overnight," he said.
In the past few years, areas along the Kosi river have suffered severe flooding, and scores of people have died.
At least 32 people were killed in a storm which hit the eastern Indian state of Bihar late on Tuesday, a government official told BBC Hindi.