A creature of statute is an entity such as a corporation created by statute.

It appears to be a legal term with meaning only in the United States: in the United Kingdom these bodies are simply called 'statutory corporations' or 'statutory bodies' and generally have some government or similar function, e.g. the UK Atomic Energy Authority. In a wider sense, most companies in the UK are created under statute since the Companies Act 1985 specifies how a company may be created by a member of the public, but these companies are not called 'statutory corporations'.