The Indian-born singer died yesterday in Pakistan at a Karachi hospital following multiple organ failure.
The 69-year-old actor, who met the ghazal maestro many times, says he is pained to learn of the news.
"Deeply pained to learn of the passing away of Mehdi Hassan, in Pakistan... A vocalist of immense fame and unique sonorous voice.
"Mehdi Hassan, an entire era of soulful ghazal singing, gone... Now left with beautiful memories and personal meetings with him...," Bachchan posted on Twitter.
The 84-year-old India-born singer was born into a family of traditional musicians at Luna village in India's Rajasthan state in 1927 and later his family migrated to Pakistan at the time of Partition in 1947.
"Mehdi Hassan once told me, he came from humble beginnings and used to train and sing to the tone of the tractor sound in the fields," Bachchan added.