What is a published false statement damaging to someone's reputation called?

A published false statement that damages someone's reputation is specifically referred to as libel. Libel is a form of defamation that involves written or published statements, as opposed to slander, which pertains to spoken statements. For a statement to be considered libelous, it must be false and injurious to the reputation of an individual or entity, thereby causing harm to their social standing or livelihood.

Defamation is the broader term that encompasses both libel and slander, but since the question specifies a published statement, libel is the most accurate term. Malice, on the other hand, refers to the intention to do harm or ill will towards another, which may be relevant in some legal contexts but does not directly define the act of making a false statement. Therefore, libel is the correct and precise answer in this context, emphasizing that the damage arises from a published medium.