The description you provided is characteristic of viruses. Viruses are non-cellular infectious agents that require a host organism to replicate. They are capable of infecting various types of organisms, including bacteria (where they are known as bacteriophages), plants, fungi, algae, and animals.
Viruses are indeed very small and possess a simple structure. When outside a host, they exist as viral particles (or virions) which consist of genetic material (either DNA or RNA) encased within a protective protein coat called a capsid. Some viruses also have an additional lipid envelope derived from the host cell membrane, but the basic structure remains the same with genetic material at its core.