Attorney Michael Avenatti, who seized the spotlight last year as a lawyer for former adult-film actress Stormy Daniels, was arrested Monday and charged with attempting to extort more than $20 million from Nike Inc., as well as bank fraud in a separate case.

Federal prosecutors in Manhattan charged Mr. Avenatti with extortion and conspiracy, alleging he told lawyers for Nike that he and an unnamed co-conspirator would release damaging information about the company if Nike didn’t pay them to conduct an “internal investigation”...