Train services in Eastern and South Eastern Railway were disrupted following lack of power supply in the overhead electrical wire, officials said.
Flight operations at NSC Bose International airport here were also hampered due to the storm.
The police said Duranto Roy (40) died on the spot when an uprooted tree fell on him during storm at Kachua Bazar in Kashipur in neighbouring South 24-Parganas district.
Roy was selling snacks at his roadside stall in the market place when the incident happened.
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Seventy-year-old Jalal Mian was declared brought dead at Howrah General Hospital after being severely injured by a uprooted tree at Banharishpur in Palchla police station in Howrah district.
Railway sources said several local trains from Howrah station were cancelled or delayed and start of journey of Mumbai Mail got delayed by more than two hours due to the storm.
Flight opeations stopped at the airport here from 7.20 pm to 8.30 pm. Several planes kept hovering in the sky and landed after the rain stopped, airport sources said.
Roads in the city were blocked by uprooted trees and traffic moved very slowly, officials said.
Member, Mayor-in-Council (Parks and Garden) of Kolkata Municipal Corporation Debasish Kumar said "seventy-five trees were uprooted in various parts of the city and KMC employees have started to clear the roads.