The diagnosis of respiratory viruses of zoonotic origin (RVsZO) such as influenza and coronaviruses in humans is crucial, because their spread and pandemic threat are the highest. Surface-enhanced Raman spectroscopy (SERS) is an analytical technique with promising impact for the point-of-care diagnosis of viruses. It has been applied to a variety of influenza A virus subtypes, such as the H1N1 and the novel coronavirus SARS-CoV-2. In this work, a review of the strategies used for the detection of RVsZO by SERS is presented. In addition, relevant information about the SERS technique, anthropozoonosis, and RVsZO is provided for a better understanding of the theme. The direct identification is based on trapping the viruses within the interstices of plasmonic nanoparticles and recording the SERS signal from gene fragments or membrane proteins. Quantitative mono- and multiplexed assays have been achieved following an indirect format through a SERS-based sandwich immunoassay. Based on this review, the development of multiplex assays that incorporate the detection of RVsZO together with their specific biomarkers and/or secondary disease biomarkers resulting from the infection progress would be desirable. These configurations could be used as a double confirmation or to evaluate the health condition of the patient.