Stage manager Debbie Williams fell from the platform just two hours before cameras were due to start rolling on the live show, hosted by Ryan Seacrest.
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Seconds later, a large tower - used as part of the set - toppled over, spraying glass across the stage.
Williams suffered a deep gash in her leg and was taken to hospital for treatment, according to People.com.
Programme-makers at FOX, FreemantleMedia North America, and 19 Entertainment said in a joint statement, "During rehearsal today a crew member had a mishap on set and was immediately taken to the hospital as a precautionary measure. We have no further information at this time."