Writing on his blog, the actor explained how he had received a request for a call from Shankar's wife Sukanya, while travelling between Morocco and Italy, IANS reports.
"She had requested a time when she could call back as Ravi Shankarji had wanted to talk to me. He was keeping unwell she had said and was to undergo a surgery on Thursday," Bachchan said.
"Due to the time difference, I was unable to connect with her immediately and it was only the next day when I called back that she spoke most endearingly and put me on to the great maestro! I was speaking to Pandit Ravi Shankar for the very first time ever on the phone."
The 70-year-actor said that Shankar praised him for his work on TV and film and he in turn offered his best wishes for the musician's impending surgery.
"We knew each other, there were strong and long family relationships, a few casual meetings, but nothing more. Why was he wanting to speak to me now? I was puzzled.
"But he came on the line, spoke with great warmth, on seeing me on the television often, of my films and my fans in the house, informed me that he was going in for a surgery - I had wished him well and after the phone call was over, sat for long, wondering how what had transpired had actually happened," he added.
Paying tribute to the world-renowned sitar maestro, Bachchan said "an entire life, an era, a most incredible period in the history of classical music in India has come to an end".
Pandit Ravi Shankar died at a San Diego hospital in the US on Tuesday.
It was announced that Shankar will receive a posthumous lifetime achievement at the forthcoming Grammy Awards.
Watch Ravi Shankar give Beatles star George Harrison a sitar lesson below: