"If you ignore the film because it's in Swedish with English subtitles, you probably deserve the remake Hollywood will surely screw up," wrote Rolling Stone magazine's Peter Travers in giving the film a 3½ of 4 possible stars.
The San Diego Union Tribune similarly urges cinema audiences to look beyond the lack of household names among the cast, its 150 minute duration, and the inconvenience of the film being in an unfamiliar Nordic tongue.
The newspaper goes as far as to suggest that Noomi Rapace should recreate her interpretation of the Lisbeth Salander character even in the Hollywood remake.
"Sure, Hollywood could translate this film into something worth watching, but it's doubtful they would make such an edgy — and risky — casting choice for the crucial role of Lisbeth (as Noomi Rapace)," the newspaper writes.
The Chicago Sun Times star critic Roger Ebert is of the same opinion.
"I can't think of an American actress who could play Lisbeth... Someone able to play hard as nails and emotionally unavailable. Make her a Swede, and simply cast Noomi Rapace."
The film is based on the first of the posthumously published Stieg Larsson trilogy of books which also includes The Girl Who Played With Fire and The Girl Who Kicked The Hornets' Nest. All three books have been made into Swedish language films, directed by the Dane Niels Arden Oplev and the Swede Daniel Alfredson.
The films are scheduled for a Hollywood remake with Steven Zaillian (Schindler's List) drafted in as screenwriter. Kristen Stewart and Ellen Page have been named as possible alternatives to play Lisbeth Salander.
Noomi Rapace received Best Actress honours at the Swedish film awards in January for her portrayal of the mesmerizing hacker-heroine, who it seems is now having the same effect on a willing US public.