The youngsters broke a window pane of Satyam Janak Place cinema hall in Janakpuri in west Delhi.
"A group of two-three youngsters were drunk and broke the glass with the aim of creating mischief. One of them was caught. They don't seem to be associated with any political party or group. They did not have any placards or posters against the movie," Deputy Commissioner of Police (west) Sharad Agarwal told.
The one who was caught was identified as 19-year-old Brij Mohan, a resident of JJ Colony in Uttam Nagar. He is a Class 11 drop-out, the police official said.
Activists of the Shiv Sena have vandalised several theatres in Mumbai that were to screen "My Name Is Khan".
The Sena is opposing the film's release after Shah Rukh refused to apologise for saying that Pakistani cricketers should have been included for the upcoming Indian Premier League (IPL) cricket matches.