What is a false statement intended to injure another's reputation called?

The correct term for a false statement intended to injure another's reputation is calumny. This term specifically refers to the act of making malicious statements about someone to damage their reputation, typically through slanderous comments that are false.

While slander and libel are also related to defamation, they refer to specific forms. Slander pertains to spoken false statements, while libel refers to written defamatory statements. Defamation is the broader legal concept that encompasses both slander and libel. Hence, calumny is used to denote the malice involved in making false claims to harm someone's reputation, which is the key aspect highlighted in the question.