The explosions were part of the latest terrorist attacks on the city, with bombs being set off during evening rush hour in Mumbai's busy Zaveri Bazar, Opera House and Dadar areas.
Actress Bachchan was set to be the special guest of the French government at a ceremony to receive the country's the Knight of the Order of Arts and Letters in recognition of her career, but postponed the event as a mark of respect for the estimated 22 people killed in the blasts.
In a statement, she says, "We are very shocked and saddened by this incident. Our prayers are with the people affected. It is important for us Indians to stand strong and tell the perpetrators of terrorism that they cannot shake us. We believe that justice will be done.
"We pray for the victims and their families. And keeping in mind what's happened, we didn't deem it prudent to celebrate. My family and I felt it would be prudent to request that the ceremony be postponed, and we thank the French government for understanding our sentiments in the current situation."