He said the pain had been "intense" after tearing two tendons a year ago, the Las Vegas Sun reported Sunday.
Doctors had wanted him to undergo surgery at that time, but Angel said he was already committed to filming a series for Spike TV and performing at the Luxor.
"There is no alternative" now, he said, after tearing the tendons a second time while hanging upside down in a strait jacket in Times Square.
"It's three times as bad now," Angel added. "I have to go under the knife. There is no other choice. I've already put it off far too long."
"Otherwise, it means permanent damage, and I wouldn't be able to ever perform again," he said.
Angel said the surgery will be performed in January and he will host a show featuring other magicians in February and March.
He expects to be performing again in April.