The disaster management team in Bihar state said 83 were killed there, while another 20 were in hospital with injuries.
At least 20 more people are reported dead in neighbouring Uttar Pradesh.
Lightning strikes are common in India during heavy monsoon rains.
Meanwhile the rain and thunderstorms have caused widespread damage to trees and property.
The authorities have warned residents to be vigilant and stay indoors, as meteorologists forecast more bad weather.
Prime Minister Narendra Modi said relief efforts were under way and expressed condolences to the victims' families.
Bihar's Disaster Management Minister Lakshmeshwar Rai told AFP this was one of the highest tolls from lightning the state had recorded in recent years. More than half the deaths were in the state's northern and eastern districts, he said.
In Uttar Pradesh most of the deaths occurred in Deoria district close to the Nepal border and the holy city of Prayagraj, authorities said.