In the film, Big B played a progeria patient, a rare condition which causes premature ageing among children. While Abhishek played his dad, Vidya Balan essayed the role of his mother on screen.
"I'm a very proud father today!!! My son just won the National Award for his performance in 'Paa'!!! (sic), " Abhishek posted on his Twitter page soon after the 57th National Film Awards were announced.
Amitabh has earlier received the prestigious award for his iconic films "Agneepath" and "Black".
"'Paa' has won four national awards!!! So excuse me for a while... going off to do the monkey dance!!! Auro, auro, auro!!!" an excited Abhishek posted.
Many from the film fraternity started posting congratulatory messages for the 67-year-old on Twitter soon after the announcement.
"Well deserved National Award for Mr. Bachchan... not that you need an award to reiterate your greatness as an actor, " posted Shilpa Shetty.
Among others who wished Bachchan were Madhur Bhandarkar, Riteish Deshmukh, Sikander Kher, Koel Purie, and Rana Duggabati.
Amitabh isn't the only one from the movie to be awarded. Theatre actress Arundhati Naag, who played his doting grandmother won the best supporting actress for the film.