Kabir, 68, who was suffering from a kidney ailment and related complications, died at 2.52 pm, a senior hospital official said.
He is survived by his wife, a daughter and a son, his son in-law Leon D’Souza said.
Kabir was appointed as the Chief Justice of India on September 29, 2012. He retired on July 19, 2013.
Born on July 19, 1948, Kabir was enrolled as an advocate in 1973 and practised in the district court and the Calcutta high court in civil and criminal sides.
He was appointed as a permanent judge in the Calcutta high court on August 6, 1990
Kabir was thereafter appointed as the Chief Justice of Jharkhand high court on March 1, 2005 and was appointed as a judge of the Supreme Court of India on September 9, 2005.
Seven years later, he was appointed as the 39th Chief Justice of India, a post he held for 292 days.
Photograph: PTI Photo