The comment enraged Bachchan and several other members, prompting Shinde to say that she was like his sister and that the remark should be deleted.
Trouble began when the home minister, who was replying to a debate on Assam violence, was interrupted by Bachchan, a well known film actor and MP from Uttar Pradesh.
Asking her to let him complete his reply, Shinde said: "Listen to me, this is not a filmy issue."
An outraged Bachchan retorted: "I strongly object to this comment."
She was backed by Leader of Opposition Arun Jaitley, who wanted the comment to be deleted.
"This is a house where people, who are achievers in a lot of fields, become members. Jayaji is an achiever in her field, the home minister of India cannot use it as a taunt," Jaitley said.
Amid the uproar from SP and other opposition members, Shinde tried to clarify what he meant. "I know her whole family, I respect her a lot. I am also from Mumbai."
He also said that the way he was interrupted was unparliamentary.
The actor-turned-politician refused to be pacified. "I cannot accept this," Bachchan said.
Shinde then said: "I apologise, she is my sister." He agreed that the remark should be deleted from the records.