Ramchandra Gandhi, a grandson of Mahatma Gandhi, was on Wednesday found dead in a room at the India International Centre (ICC) in New Delhi.
The body of Gandhi (70) was found in Room number 15 of the elite club in South Delhi where he had checked in on June 10, a senior police official said.
The housekeeping staff knocked at the door of the room in the morning on Wednesday and after not getting any response informed the manager about it.
The door was then broken open and Gandhi's body was found lying on the floor.
Police said the room was locked from inside so they did not suspect any foul play and prima facie it appeared to be a natural death.
The family of the deceased, who was a resident of Bengali Market in the capital, told the police that Gandhi, an ex-member of the club, had checked into the IIC because of the heat.
The body was likely to be sent for post-mortem, the official said.
Gandhi was a former professor at Princeton University. He was the elder brother of West Bengal Governor Gopal Krishna Gandhi.