"Hindustani classical music has lost one of its stalwarts of the Gwalior gharana. She had the rare opportunity to be trained by some of the best gurus of classical music in India," Gandhi said in a statement.
"Her contribution to classical music education with her music appreciation courses in colleges across India had significant popularity and is a noteworthy contribution," she added.
Expressing solidarity with members of her family, students and those who admired her work. Gandhi said, "India's most authentic exponent of the Gwalior gayaki leaves a rich legacy behind, that will be cherished forever."
Sahasrabuddhe died on Wednesday after a prolonged illness.
She was a leading Indian vocalist and composer of Hindustani classical music. Her singing style had its roots in Gwalior gharana, but it also borrowed from Jaipur and Kirana gharanas.
Veena was known as a singer of khyal and bhajan.