The group - consisting of Niall Horan, 18, Harry Styles, 18, Zayn Malik, 19, Louis Tomlinson, 20 and Liam Payne, 18 - hoped to watch ex-Playmate Holly Madison in her Peep Show performance.
However, tour managers said the boys won't have time to pay the 32-year-old a visit.
Once they have played The Performing Arts Centre last Saturday night , they have to go immediately to Phoenix, Arizona, which is six hours away, for promotional work the next day.
A source told the Daily Star: "One Direction are not happy. The MGM chiefs offered them the works, and Holly loves the boys.
"She wanted to give them a special show and even get them backstage to meet all the girls.
The insider added: "Harry especially would have been like a kid in a candy shop. But they are not able to fit in the show and make the schedule for Phoenix.
"For most of the time in the States it's been all work for the lads and not much play. This would have been a nice distraction."