The drug-themed movie, released on June 17, had courted controversy after Central Board of Film Certification asked for multiple cuts.
However, the film was passed by the Bombay High Court with just a revised disclaimer and omission of one scene.
"Humbled and thankful. Your love has been overwhelming. More power to honest fearless cinema. Thank you all," Shahid wrote.
The Abhishek Chaubey-directed Punjab-set crime drama also earned Rs 10.05 crore on its opening day.
'Udta Punjab' talks about the issue of substance abuse in the state of Punjab through the stories of a high-on-drugs rockstar (Kapoor), a migrant (Alia Bhatt), a doctor (Kareena Kapoor Khan) and a policeman (Diljit Dosanjh).