Jaya Smriti is organised every year since 2010 by the 64-year-old actress in remembrance of her mother Jaya Chakravarthi, who encouraged her to take up bharatanatyam.
Malini inaugurated the event at the Nehru Center here on Friday but postponed the next two days' programme following Thackeray's death on Saturday.
"Due to sad demise of Shri B Thackeray, Jaya Smriti on 17 & 18 Nov is postponed. I hope you all who love me will stand by me in this situation," Malini posted on Twitter.
The new dates for the music and dance event are yet to be announced.
This year, the festival was scheduled to host performances by budding Indian classical dancers, besides workshops on Odissi and Kathak.
Malini's company, Natyavihar Kalakendra also plans to stage two productions as well as music recitals at the event.