She breathed her last late on Monday night at the Breach Candy Hospital where she was admitted recently for treatment of some lung ailments, but details are not available.
She was 71 and is survived by her husband Adi Godrej and their three children, Nisaba Godrej, Pirojsha and Tanya Dubash.
The last rites of Parmeshwar were performed in Mumbai early on Tuesday.
Parmeshwar started her career as one of the first airhostesses of national carrier Air India, before she married Godrej and became a prominent figure in the city's glam and celeb circuits.
She was renowned for her work in combating AIDS through the Heroes Project which she launched in 2004 along with Hollywood actor Richard Gere and supported by the Bill & Melinda Gates Foundation and Clinton Global Initiative and also served on the board of several major international foundations and trusts.
A popular socialite with the signature beret, and once a Page 3 regular, Parmeshwar had hosted a party for international talk show queen Oprah Winfrey in 2012.
The news of her demise was received on Tuesday with shock and disbelief by friends and celebrities.
Former Union Minister Milind Deora tweeted: "Deepest condolences to Adi uncle, Tanya, Nisaba, Pirojsha and family. Will miss Parmeshwar Godrej, one of the warmest, toughest people I knew."
Pakistani cricketer-turned-politician Imran Khan tweeted the news of her death.
"Devastated by death of close friend Parmeshwar Godrej... she was always there for me in my most difficult times. May her husband Adi and her children find strength to cope with this loss," he wrote.
Members of the Hindi film fraternity also mourned her death. Shah Rukh Khan tweeted:Not how she looked, not wot she said but just by being wot she was, my most beautiful friend Parmesh,I will miss ur kisses & ur light. RIP
Filmmaker Madhur Bhandarkar tweeted: "One of the most gracious and down to earth person I knew. You will be missed."
Veteran actor Kabir Bedi posted: "Deeply saddened by the passing of Parmeshwar Godrej, dear friend from my early days in advertising. I share her family's grief."
Anupam Kher wrote: "Parmeshwar Godrej was a larger than life lady. She gave style and glamour a new dimension. Her charity work was great."
Jewellery designer Farah Khan said: "Lost a close family friend. My childhood years were filled with her memories. RIP Parmeshwar Aunty, you shall be missed Parmeshwar Godrej."
Filmaker Karan Johar tweeted:
IANS