Approximately 40 minutes of the movie footage is available online with 'for censor' written on the top left corner, according to websites.
There are also reports that the entire movie, which has a running time of 2 hours 20 minutes, is doing the rounds on movie downloading sites.
However, when contacted a source from the film's team said they have managed to remove the leaked links.
The film's co-producer Anurag Kashyap was at the forefront of the fight against the Central Board of Film Certification (CBFC), which had asked for multiple cuts in the drug-themed drama, directed by Abhishek Chaubey.
The producers had moved the Bombay High Court against the the board's decision. The court cleared the film for release with just one cut.
'Udta Punjab', starring Shahid Kapoor, Kareena Kapoor, Alia Bhatt and Diljit Dosanjh, will release this Friday.