The New York attorney general’s office has subpoenaed more than a dozen advocacy groups, lobbying firms and consultants as part of an investigation of fake comments filed with the Federal Communications Commission over its proposal to scale back its regulation of the internet.

The civil subpoenas are aimed at determining who was behind millions of comments sent using the names of real people who didn’t authorize them, according to a person familiar with the investigation. New York Attorney General Barbara Underwood said in...