Aaradhya is Amitabh's son Abhishek and daughter-in-law Aishwarya Rai's daughter. She will turn 2 on Nov 16.
"The little one climbing up to my room to enquire after my health in a language only she would best understand," Bachchan posted on his blog srbachchan.tumblr.com late Wednesday night.
The 71-year-old, who may take four more days to get perfectly fine, says he has been resting to the best of his ability.
"Not moved from my recline the entire day, despite meetings which were most imperative to have... cricket kept me involved entirely," he added.
Amitabh is currently seen on popular TV game show "Kaun Banega Crorepati".