There is an urgent need to find new solutions for the global dilemma of increasing antibiotic resistance in humans and animals. Modifying the performance of existing antibiotics using the nanocarrier drug delivery system (DDS) is a good option considering economic costs, labor costs, and time investment compared to the development of new antibiotics. Numerous studies on nanomedicine carriers that can be used for humans are available in the literature, but relatively few studies have been reported specifically for veterinary pharmaceutical products. Polymer-based nano-DDS are becoming a research hotspot in the pharmaceutical industry owing to their advantages, such as stability and modifiability. This review presents current research progress on polymer-based nanodelivery systems for veterinary antimicrobial drugs, focusing on the role of polymeric materials in enhancing drug performance. The use of polymer-based nanoformulations improves treatment compliance in livestock and companion animals, thereby reducing the workload of managers. Although promising advances have been made, many obstacles remain to be addressed before nanoformulations can be used in a clinical setting. Some crucial issues currently facing this field, including toxicity, quality control, and mass production, are discussed in this review. With the continuous optimization of nanotechnology, polymer-based DDS has shown its potential in reducing antibiotic resistance to veterinary medicines.