Most of the people who died were working on farms during torrential rains on Tuesday, reports said.
Lightning strikes are common in India during heavy monsoon rains.
Fifty-six people died in Bihar while 37 people were killed across Uttar Pradesh, Jharkand and Madhya Pradesh.
"Many of the victims are children and women," Anirudh Kumar, a senior official at Bihar's disaster management agency, told AFP news agency.
One man taken to hospital in Rohtas said: "When it was raining, we immediately took shelter. It [lightning] hit us there, and then we fell unconscious.
"We could not understand what had happened. Then in the middle, when I regained consciousness, I realised that I had been hit by something."
Indian Prime Minister Narendra Modi said he was "deeply anguished" by the loss of life.
At least 2,000 people have died in lightning strikes in India every year since 2005, according to the National Crime Records Bureau.
India receives 80% of its annual rainfall during the monsoon season, which runs between June and September.
Source: Royal Society for the Prevention of Accidents
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At least 93 people have been killed and more than 20 injured by lightning strikes in the Indian states of Bihar, Jharkhand, Uttar Pradesh and Madhya Pradesh, officials say.