Faiz Usmani was taken to hospital by police when he complained of feeling unwell due to hypertension. Usmani was not a suspect in the Mumbai blasts but was quizzed due to his connections with alleged Indian Islamist militants.
"We hardly questioned him for an hour. There is no question of torture, we just asked him a few questions," Mumbai police spokesman Nisar Tamboli told the NDTV news channel.
"He was on medication and had not taken his medicines for three to four days."
But Usmani's son told the Press Trust of India (PTI) news agency that the police "are to blame for his death".
"My father was picked up for questioning and pressurised during interrogation," he said.
Ryan Kumar, a doctor at the Lokmanya Tilak hospital in Mumbai, told NDTV that Usmani died of a brain haemorrhage, adding that "this usually happens when an otherwise normal person is subjected to a shock or mental disturbance".
Police said a post-mortem report would be prepared and an inquiry had been launched.
There have been no claims of responsibility for Wednesday's rush-hour attack on Mumbai, which killed 19 and injured more than 130 people.
Police have been questioning suspected members of the Indian Mujahideen, a domestic Islamist group with links to Lashkar-e-Taiba, the Pakistan-based militant outfit blamed for the 2008 Mumbai attacks when 166 people died.
Usmani's brother, Afzal Usmani, is in custody on suspicion of being part of an Indian Mujahideen team which carried out a string of deadly bomb blasts in the western state of Gujarat in July 2008.