"Rajnikant coming over to Mumbai to show us 'Robot'... which incidentally has become a storm all over the country, " Amitabh Bachchan wrote on microblogging site Twitter.
The film also stars Aishwarya Rai in the lead. Made at a budget of Rs.175 crore ($38 million), it's the costliest Indian film ever.
"Just exceptional its business and its talk all over!! Happy for Rajni and of course for Aishwarya ... the film has broken all time records!!" wrote Big B.
The special screening is scheduled for Monday.