Shortly after introducing the nine-year-old white tiger, it lunged at German-born Roy Horn, who tried to beat him off with a microphone.
The tiger went for his neck and then dragged him offstage, said audience member Andy Cushman. "He looked like a rag doll."
Horn was rushed to the University Medical Centre, which said later he was out of surgery but still in critical condition.
Horn's partner Siegfried Fisbacher appeared on stage moments later, visibly upset, and cancelled the remainder of the show.
The tiger was being held in quarantine at the hotel, a spokesman for the performers told the LA Times newspaper.
It was the first public performance for the tiger.
"The last place Roy would place blame would be with the animal," said Berni Yuman, manager of Siegfried and Roy.
The illusionists perform eight shows a week in a 1,504-theatre that bears their name at the Mirage Hotel. The hotel has a lifetime contract with the duo.