Skin wounds and their infections by antibiotic-resistant bacteria (ARB) are very common in small animals, posing the risk of acquiring ARB by pet owners or antibiotic resistance gene (ARG) transfer to the owners’ microbiota. The aim of this study was to identify the most common pathogens infecting wounds of companion animals, assess their antibiotic resistance, and determine the ARGs using culture-based, molecular, and proteomic methods. A total of 136 bacterial strains were isolated from wound swabs. Their species was identified using chromogenic media, followed by MALDI-TOF spectrometry. Antibiotic resistance was tested using disc diffusion, and twelve ARGs were detected using PCRs. The dominant species included Staphylococcus pseudintermedius (9.56%), E. coli, and E. faecalis (both n = 11, 8.09%). Enterobacterales were mostly resistant to amoxicillin/clavulanic acid (68.3% strains), all Pseudomonas were resistant to ceftazidime, piperacillin/tazobactam, imipenem, and tylosin, Acinetobacter were mostly resistant to tylosin (55.5%), all Enterococcus were resistant to imipenem, and 39.2% of Staphylococci were resistant to clindamycin. Among ARGs, strA (streptomycin resistance), sul3 (sulfonamide resistance), and blaTEM, an extended-spectrum beta-lactamase determinant, were the most frequent. The risk of ARB and ARG transfer between animals and humans causes the need to search for new antimicrobial therapies in future veterinary medicine.