The 69-year-old actor wrote about the incident in his blog, saying that the person is in the custody of the police, who are now investigating the case.
"Spent some anxious moments yesterday since we had a break in! The guy was caught and is with the police now under investigation. Seems like a professional, for he had entered the most sensitive area of the house, Jalsa," Amitabh posted.
"Cops and security are in over drive now. In the end nothing is secure, irrespective of how much precaution one takes," he added.
The Bachchan family has three bungalows - Jalsa, Prateeksha and Janak, within walking distance of each other, at Juhu, Mumbai.
Jalsa is the new house where Amitabh and Jaya live with son Abhishek, daughter-in-law Aishwarya and grand-daughter Aaradhya while younger brother Ajitabh lives in Prateeksha.
Janak is used as the Bachchan office. Janak also has a gym which the Bachchan's use regularly.