Dikshit passed away at a private hospital here following a cardiac arrest. She was 81.
Mangeshkar recalled her conversations with Dikshit on music and poetry.
"A remarkable woman, former CM of New Delhi and a keen admirer of all art forms. We never discussed politics but had long talks on music and poetry. May her soul rest in peace, and heartfelt condolences to her family," Mangeshkar tweeted.
Akshay praised Dikshit for her contribution to the national Capital.
"Extremely sad to know about the passing away of Sheila Dikshitji... she effectively changed the face of Delhi during her tenure. Heartfelt condolences to her family," he wrote. Bhumi Pednekar wrote: A great leader indeed... My condolences to the family. You were so loved ma'am. A great loss to our nation. May your soul rest in peace.
Nimrat Kaur called Dikshit a "lady par excellene".
She wrote: "Deepest condolences and heartfelt prayers on the passing of Sheila Dikshitji. A lady par excellence, someone who lead by example. An indispensable presence for generations to remember. May her blessed soul rest in peace."
Actress Richa Chadha considered Dikshit's death as "a personal loss to anyone who grew up in Delhi".
"During my school and college, the green cover of Delhi actually grew by 300 per cent ! A tall leader. Rest in peace ma'am. Condolences to family," she added.
Bhangra star Mika Singh wrote: "Very sad news.. Our Ex Chief Minister of Delhi, Sheila Dikshit, has sadly passed but has left us with her beautiful memories... May God bless her soul, Rest in peace."
Isha Koppikar sadi she was "deeply saddened".
"Deeply saddened by the news of Sheila Dikshitji passing away. I offer my deepest condolences, and may her soul rest in peace," Isha wrote.
Dikshit is given credit 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. She had also been Kerala Governor briefly in 2014.
( With inputs from IANS )