The present study aimed to determine the phenotypic and genotypic characteristics of S. aureus isolates from the nasal swabs of goats. A total of 232 nasal samples (one per animal) were collected from goats on 13 farms located in two regions of Algeria and were analyzed for the presence of S. aureus. The detection of virulence factors was carried out using PCR. The antibiotic susceptibility of the recovered isolates was assessed using the disc diffusion method. The biofilm formation ability was assessed by the Congo red agar method and a microtiter plate assay, and the molecular characterization of isolates was carried out by spa-typing, and for selected isolates also by multilocus sequence typing (MLST). Overall, 36 out of 232 nasal swabs (15.5%) contained S. aureus, and 62 isolates were recovered. Regarding the virulence factors, at least one staphylococcal enterotoxin gene was detected in 30 (48.4%) isolates. The gene tst encoding the toxic shock syndrome toxin was detected in fifteen isolates (24.2%), but none of the isolates harbored the gene of Panton–Valentine leukocidin (lukF/S-PV). Nine different spa-types were identified, including the detection of a new one (t21230). The recovered isolates were assigned to three clonal complexes, with CC5 (51.8%) being the most common lineage. Two isolates were methicillin-resistant (MRSA) and belonged to ST5 (CC5) and to spa-types t450 and t688. Moreover, 27 (43.5%) of the S. aureus isolates were found to be slime producers in Congo red agar, and all of the recovered isolates could produce biofilms in the microtiter plate assay. Our study showed that the nares of healthy goats could be a reservoir of toxigenic and antibiotic-resistant strains of S. aureus isolates, including MRSA, which could have implications for public health.