MELBOURNE, Australia—More than 20 Australian journalists, including editors of major newspapers, face possible prison terms and fines for allegedly breaching a judicial order suppressing coverage of a top Vatican official’s conviction for child sex abuse.

Prosecutors have accused some of the country’s largest newspapers, radio stations and online media groups of contempt of court for publishing news of Cardinal George Pell’s guilty verdict in December on five counts of sexually abusing two choir boys in the 1990s. The contempt...