Among the 13 injured are four members of his family.
The deceased, identified as Suhail, died after wall in his house collapsed on him while he was sleeping, PTI quoted the police as saying.
Wednesday's storm was the second of its kind to hit the national capital in the past four days.
The heavy rain and dust storm hit Delhi-NCR on Wednesday early morning. The police received almost 60 calls related to uprooted trees, fallen electricity polls and wall collapses across the region.
According to Indian Meteorological Department (IMD), dust storms accompanied with strong winds and lightning are likely to hit Delhi and it's adjacent areas which include Rohtak, Manesar, Gurgaon, Sonepat and Meerut in the next two hours.
Strong winds, accompanied by dust, lashed the city while bringing a sudden decline in the temperature.
Thunderstorms, dust storms, rainfall during summers have been a normal phenomenon in northern India.
Earlier on Tuesday, India Meteorological Department (IMD) had predicted severe weather conditions in several parts of Rajasthan, Uttarakhand, Jammu and Kashmir and Himachal Pradesh. "But not of this severity". Almost two weeks ago, 134 people were killed while 400 others were injured after a massive dust and thunderstorm hit Uttar Pradesh, Rajasthan, Telangana, Uttarakhand and Punjab. "The frequency of western disturbance is unusually high", said Mahesh Pahlawat, vice-president (Meteorology and Climate Change) at Skymet, reported The Indian Express.
It uprooted trees and caused power outages at several parts.
A wave of sandstorms and thunderstorms sweeping through in India have left at least 86 people dead and 100 others injured, authorities said Monday.