According to the Fortis Escorts Heart Institute, Dikshit, who was Chief Minister for three consecutive terms (1998-2013), suffered cardiac arrest and was brought to the hospital on Saturday morning in a critical condition.
A multi-disciplinary team of doctors carried out advanced resuscitative measures on her, it said.
"Her condition stabilised temporarily. However, she had another cardiac arrest and despite all the resuscitative efforts, passed away at 3.55 p.m.," the hospital added.
Credited for Delhi's growing infrastructure including roads and flyovers, better public transport system - especially the Delhi Metro, as well as development on the health and educational fronts, during her tenure, Dikshit had also been Kerala Governor briefly in 2014.
Heading the Congress' Delhi unit since January this year, she had also contested the 2019 Lok Sabha polls unsuccessfully.
Leaders from across the political spectrum paid her tributes for her contribution to Delhi's development.
President Ram Nath Kovind condoled her demise, saying she had transformed the national capital in her tenure.
Prime Minister Narendra Modi also credited her with noteworthy contribution to Delhi's development.
Delhi Chief Minister Arvind Kejriwal on Saturday mourned the death of his predecessor, saying Dikshit's contribution to the city will always be remembered.