Spielberg typically keeps the plot points of his films closely guarded before their release, and Minority Report was no different. He said he had to remove some scenes, and a few "F-words" to get the film's PG-13 rating. Following the disappointing box office results of Spielberg's A.I., the marketing campaign for Minority Report downplayed his role in the movie and sold the film as a Cruise action thriller.
Tom Rothman, chairman of the film's co-financier Fox Filmed Entertainment, described the film's marketing strategy thus: "How are we marketing it? It's Cruise and Spielberg. What else do we need to do?" The strategy made sense; coming into the film, Spielberg had made 20 films which grossed a domestic total of $2.8 billion, while Cruise's resume featured 23 films and $2 billion in domestic revenues. With their combined 30% take of the film's box office though, sources such as BusinessWeek's Ron Grover predicted the studios would have a hard time making the money needed to break even. Despite the outward optimism, as a more adult-oriented, darker film than typical blockbusters, the studio held different box office expectations for the movie than they would a more family friendly film. Entertainment Weekly projected the film would gross $40 million domestic in its opening weekend, and Variety predicted that the high concept storyline would not appeal to children and would render it a "commercial extra-base hit rather than a home run."
Minority Report's world premiere took place in New York City on 19 June 2002. An online "popcorn cam" broadcast live from inside the premiere. Cruise attended the London premiere the following week, and mingled with thousands of adoring fans as he walked through the city's Leicester Square. It debuted at first place in the U.S. box office, collecting $35.677 million in its opening weekend. Forbes considered those numbers below expectations, as they gave the film a small edge over Lilo & Stitch, which debuted in second place ($35.260 million). Lilo & Stitch sold more tickets, but since much of the film's attendees were children, its average ticket price was much lower. The movie opened at the top of the box office in numerous foreign markets; it made $6.7 million in 780 locations in Germany its opening weekend, and accounted for 35% of France's total box office weekend office gross when it collected $5 million in 700 theaters. In Great Britain, Minority Report made $36.9 million in its first three days, in Italy, $6.2 million in its first ten, in Belgium, $815,000 in its 75 location opening weekend, and in Switzerland, $405,000 in an 80 theater opening weekend. The BBC felt the film's UK performance was "buoyed by Cruise's charm offensive at last week's London premiere." Minority Report made a total of $132 million in the United States and $226.3 million overseas.
DreamWorks spent several million dollars marketing the film's DVD and VHS releases. The campaign included a tie-in video game released by Activision, which contained a trailer for the movie's DVD. Minority Report was successful in the home video market, selling at least four million DVDs in its first few months of release. The DVD took two years to produce. For the first time, Spielberg allowed filmmakers to shoot footage on the set of one of his films. Premiere-award winning DVD producer Laurent Bouzereau, who would become a frequent Spielberg DVD collaborator, shot hundreds of hours of the film's production in the then-new high-definition video format. It contained over an hour of featurettes which discussed various aspects of film production, included breakdowns of the film's stunt sequences, and new interviews with Spielberg, Cruise, and other "Academy Award-winning filmmakers". The film was released on a two-disc Blu-ray by Paramount Pictures (now the owner of the early DreamWorks library) on 16 May 2010. It included exclusive extras and interactive features, such as a new Spielberg interview, that were not included in the DVD edition. The film was transferred from its "HD master" which retained the movie's distinctive grainy appearance.
A video game based on the film titled Minority Report: Everybody Runs was developed by Treyarch, published by Activision and released on 18 November 2002 for Game Boy Advance, Nintendo GameCube, PlayStation 2 and Xbox. It received mixed reviews.