Johansson, 21, had been targeted to play Maria von Trapp in Andrew Lloyd Webber's production of the Rodgers and Hammerstein musical, set to open in London's West End in November.
"Her people were not `pro' the idea. It became clear that it wasn't going to work because the demands were so ridiculous," Lloyd Webber was quoted as saying in The Times newspaper.
He said Johansson's representatives "couldn't understand why she would want to appear in the West End for $18,500 a week when she could be earning $10 million for a movie."
"It was annoying because she really wanted to do it," Lloyd Webber was quoted as saying.
Publicist Marcel Parisbeau said it was a busy work schedule and not pay demands that sank the actress' chance to play the role made famous by Julie Andrews in the 1965 film version of the musical.
"It is true that there were some discussions regarding Scarlett and the production of `The Sound of Music.' But Mr. Webber's statement regarding the demands is extremely exaggerated," Parisbeau said in a statement. "Her management team was simply asking for terms that an actress of her stature would ask for."
Lloyd Webber said he was also told that Johansson would need two assistants stationed backstage at all times, according to the report.
The role of Maria will now be played by an actress to be chosen from a new British Broadcasting Corp. reality TV show. The Aug. 15 finale of "How Do You Solve a Problem Like Maria" will award a six-month contract to one of 10 finalists.
Johannson stars in Woody Allen's new movie, "Scoop," set to open Friday. Her screen credits also include roles in "Lost in Translation" and "Girl With a Pearl Earring."