Mr. Daniels’s success at singing high parts that were once the province of castratos or mezzo-sopranos helped inspire a new generation of countertenors — and added fuel to revival of works by Handel, which provided him with some of his best roles at the Metropolitan Opera and with companies around the world. The accusation against him is the latest instance of the classical music industry grappling with allegations of sexual misconduct; over the past year, the conductors James Levine, Charles Dutoit and Daniele Gatti have been accused of inappropriate behavior.

The accusation against Mr. Daniels came to light after Mr. Schultz posted an account online in which he wrote that “a celebrated opera singer and his boyfriend raped me,” but the account did not include names. In it, Mr. Schultz said he had been afraid to come forward sooner, in part because it could have harmed his career. But he said he hoped to inspire “others to come forward and say #MeToo.”

In the interview, Mr. Schultz said the incident had occurred in May 2010, just after he had finished his first year in graduate school at Rice University in Houston. He said he had been introduced to Mr. Daniels and Mr. Walters by a friend, and had attended the final night of Handel’s “Xerxes” and the cast party afterward. Then, he said, he was invited to Mr. Daniels and Mr. Walters’s apartment. There, Mr. Schultz said, they gave him a drink that caused him to lose consciousness. When he woke up the next afternoon, he said in a statement that he has shared with the police, he was alone in the apartment, naked and bleeding from his rectum.

When Mr. Daniels returned, Mr. Schultz said, Mr. Daniels made a remark that Mr. Schultz understood to mean that they had had sex without a condom.

Mr. Schultz has gone on to sing with Washington National Opera, Houston Grand Opera and other companies. He said that while he told his family, his therapist and some friends about what happened, he had been afraid to come forward before now.