The 15-year-old's photoshoot for the cover of the magazine's forthcoming issue has sparked outrage in the US.
The website logged more than four million hits yesterday as users tried to view the snap, in which the Hannah Montana star appears wrapped in only a blanket. It was forced to shut down at one stage due to the volume of internet traffic.
The scandal comes just a week after candid photographs of the teenager in her underwear were leaked online.
Jamie Lee Curtis earlier defended Cyrus, while photographer Annie Leibovitz said the shot was "misinterpreted".