Viruses have a high mutation rate, and, thus, there is a continual emergence of new antiviral-resistant strains. Therefore, it becomes imperative to explore and develop new antiviral compounds continually. The search for pharmacological substances of plant origin that are effective against animal viruses, which have a high mortality rate or cause large economic losses, has garnered interest in the last few decades. This systematic review compiles 130 plant species that exhibit antiviral activity on 37 different virus species causing serious diseases in animals. The kind of extract, fraction, or compound exhibiting the antiviral activity and the design of the trial were particularly considered for review. The literature revealed details regarding plant species exhibiting antiviral activities against pathogenic animal virus species of the following families–Herpesviridae, Orthomyxoviridae, Paramyxoviridae, Parvoviridae, Poxviridae, Nimaviridae, Coronaviridae, Reoviridae, and Rhabdoviridae–that cause infections, among others, in poultry, cattle, pigs, horses, shrimps, and fish. Overall, 30 plant species exhibited activity against various influenza viruses, most of them causing avian influenza. Furthermore, 30 plant species were noted to be active against Newcastle disease virus. In addition, regarding the pathogens most frequently investigated, this review provides a compilation of 20 plant species active against bovine herpesvirus, 16 against fowlpox virus, 12 against white spot syndrome virus in marine shrimps, and 10 against suide herpesvirus. Nevertheless, some plant extracts, particularly their compounds, are promising candidates for the development of new antiviral remedies, which are urgently required.