A storm with wind speeds of up to 90 kilometres per hour hit the Indian capital on Friday night, uprooting trees, blowing down billboards and causing traffic jams across the city.
"At least nine people died and over a dozen were injured in storm-related accidents," Delhi police spokesman Jagbir Singh said.
"The deaths were reported in accidents like falling trees, collapsed walls and electrocution," he said.
Seven deaths each were reported from the eastern state of Jharkhand and West Bengal, which was also hit by storms early Saturday morning, the online edition of Times of India and broadcaster NDTV reported.
Several deaths were reportedly due to lightning strikes.
During Friday night's storm in Delhi, five aircraft parked at the city's international airport were damaged while 21 flights, including four international flights, were diverted to other cities after failing to land in the dust-shrouded capital, the IANS news agency reported.
Many areas of the city plunged into darkness as the storm snapped power lines. Metro train services were disrupted for about an hour due to power failure.
Some local trains were cancelled and long distance trains delayed by half an hour, railway officials said. Power was restored by late Friday night.
Indian weather officials said intense heat and cyclonic conditions in north India were likely to persist for the next few days.
India's northern, western and eastern regions are experiencing a heatwave Delhi saw its hottest day in 16 years when the mercury touched 46 degrees Celsius on Thursday.