The first tremor struck in Gujarat and another was felt just two hours later in Maharasthra, according to local reports.
Veteran actor Bachchan, who is currently in Mumbai, felt the effects of one of the quakes and took to his Twitter page to assure followers he was Ok.
He tweeted, "Earthquake in Mumbai!! Did you feel it... I did! Shutters and building shook twice for few seconds... all good here... all else?
"I hope and pray everyone is safe!! Peace and happiness... stay well!"
Irish singer Ronan Keating also sent his prayers to the people of India, writing, "Just heard about the earthquake in Mumbai. God bless them at this time."
There were no reports of injury after the double disaster.