The Police Control Room or PCR received 78 phone calls during the storm that started at around 3 am.
One person was injured in Dwarka while two people sustained minor injuries in west Delhi during the storm.
The deceased was identified as Sohail a resident of north east Delhi's Gokal Puri area.
He got injured after a wall collapsed on him while he was sleeping in his house. Four members of his family have also sustained minor injuries, police said.
Four persons were injured in east Delhi while two persons sustained minor injuries in south Delhi, they added.
Four calls that the police received were about damages to cars in the dust storm. Fourteen vehicles - 13 cars and a motorcycle - were damaged in it, the police said.
As per the traffic control room, as many 53 calls related to falling of trees and six calls about fallen poles were received during dust storm the previous night.
Thirty-seven fallen trees have been removed and remaining are being removed, officials said.