One man was killed and another one injured when part of the stage roof crashed onto a construction crew at Marseille's Stade Velodrome.
A French worker was killed immediately after suffering injuries in a fall of nearly 50ft (15m), a local newspaper said.
Madonna's planned concert on Sunday was cancelled.
Two other workers, one British and one American, remain in a serious condition, the media said.
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In a statement on her website, Madonna, who is now on the Italian leg of her Sticky And Sweet world tour, said: "I am devastated to have just received this tragic news.
"My prayers go out to those who were injured and their families along with my deepest sympathy to all those affected by this heart-breaking news."