The introduction of new regenerative therapeutic modalities in the veterinary practice has recently picked up a lot of interest. Stem cells are undifferentiated cells with a high capacity to self-renew and develop into tissue cells with specific roles. Hence, they are an effective therapeutic option to ameliorate the ability of the body to repair and engineer damaged tissues. Currently, based on their facile isolation and culture procedures and the absence of ethical concerns with their use, mesenchymal stem cells (MSCs) are the most promising stem cell type for therapeutic applications. They are becoming more and more well-known in veterinary medicine because of their exceptional immunomodulatory capabilities. However, their implementation on the clinical scale is still challenging. These limitations to their use in diverse affections in different animals drive the advancement of these therapies. In the present article, we discuss the ability of MSCs as a potent therapeutic modality for the engineering of different animals’ tissues including the heart, skin, digestive system (mouth, teeth, gastrointestinal tract, and liver), musculoskeletal system (tendons, ligaments, joints, muscles, and nerves), kidneys, respiratory system, and eyes based on the existing knowledge. Moreover, we highlighted the promises of the implementation of MSCs in clinical use in veterinary practice.