"I am extremely disturbed and concerned about the critical health of Shri Balasaaheb Thackeray, who is like a family member to me. My prayers are with Balasaaheb and the entire Thackeray family," Mangeshkar wrote on Twitter.
"In view of this, I am postponing the function of my music company to a later date," Mangeshkar said.
The event was scheduled for November 18.
Meanwhile, Bollywood celebrities Madhur Bhandarkar, Nana Patekar and others visited Thackeray's residence 'Matoshree' in suburban Bandra.
Filmmaker Pritish Nandy said he is praying for Thackeray's recovery.
"My sympathies and love to Uddhav and Aditya as they cope with the tragedy of Balasaheb's failing health. May he fight back and win. Our prayers go out for Balasaheb Thackeray and his family members.... May the tiger wake up and roar again," he said.
"That a cartoonist in the Free Press Journal could reach where Balasaheb reached is a tribute to the power of Indian democracy. There will be lots of time later to discuss the politics of the Sena, good or bad. Time to now pray that Balasaheb comes back from the edge," he added.
Filmmaker Ashok Pandit tweeted, "Balasahab stopped my community (Kashmiri pandits) from picking up arms by giving us education. After my exodus, I went to Balasaheb for help. He asked me wht do u want? I said our wealth is education. He immed creating a quota & gve us edu (sic)."