According to attendees of his Mindfreak Live! show at the Luxor Hotel in Las Vegas, the incident occurred just minutes into the show.
Angel was dangling upside-down over the stage, trying to break free of his straightjacket, when he suddenly went limp.
"He was wiggling, trying to break loose of the straitjacket while suspended, turning in circles really fast, and he just kept trying to wriggle free," Ryan Perez, a 16-year-old who went to the show with his family, told BuzzFeed News. "And with five seconds left, he suddenly stopped moving."
Cast members then brought a stool on stage, untied Angel, and rushed him offstage. They could be heard yelling offstage "like they were scrambling to make sure he was OK," Ryan said.
There was an intermission, and five minutes later it was announced that the show was being cancelled and all tickets would be refunded.
In a statement posted to Angel's Twitter account on Saturday, his team said the magician was undergoing additional tests, and that he hoped to return to the stage soon. However, the statement did not address a potential cause of him losing consciousness.