"Even in Hollywood there seems to be a kind of anger about the remake," Niels Arden Oplev said in an interview with the Word and Film website.
Sweden's Michael Nyqvist and Noomi Rapace starred in the original film, released in the UK earlier this year.
Britain's Daniel Craig and newcomer Rooney Mara co-star in the US version.
Currently shooting in Stockholm, the remake is being directed by David Fincher of Fight Club and The Social Network fame.
It is due out in cinemas in December 2011.
In Larsson's novel and its two sequels, an investigative journalist joins forces with a female computer hacker to solve crimes.
Both sequels have been filmed in Sweden with Nyqvist and Rapace reprising their roles as Mikael Blomkvist and Lisbeth Salander.
According to Word and Film, Oplev is concerned that Mara's peformance will overshadow Rapace's.
"The Sony PR machine is trying to make their Lisbeth Salander the lead Lisbeth Salander," he is quoted as saying.
"That's highly unfair because Noomi has captured this part and it should always be all her," he goes on.
"That's her legacy in a way I can't see anyone competing with. I hope she gets nominated for an Oscar."
The Swedish Girl with the Dragon Tattoo film made Â£2.2m in the UK and $10.1m (Â£6.2m) in the US.
Its follow-up, The Girl who Played with Fire, came out in August, while a third film, The Girl Who Kicked The Hornet's Nest, is released this month.
Larsson did not live to see his Millennium trilogy of crime novels become an international publishing sensation.
The Swedish author and journalist died of a heart attack in November 2004 at the age of 50.

The Kilkenny fighter floored Richards twice before another standing count for the Swede quickly ended the contest.
O'Neill, 30, will now take on top seed Abdulkadir Abdullayev from Azerbaijan for a place in the semi-finals.
The top three men will earn a place for their country in their division at the Rio Games this summer.
David Oliver Joyce had a unanimous points victory over Otar Eranosyan from Georgia in the lightweight division.
But world bronze medallist Michael O'Reilly, the number one seed in the middleweight class, lost to Ilari Kijala of Finland in a unanimous points decision.
The Danish director of The Girl with the Dragon Tattoo has questioned why an English-language version is being made of Stieg Larsson's best-selling novel.
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Ireland's Darren O'Neill stopped Gabriel Richards in the first round at the European Olympic Qualifying event in Samsun, Turkey, on Tuesday.