Leprosy, characterized by dermatological manifestations and peripheral nervous system impairment due to Mycobacterium leprae infection in Schwann cells, poses persistent challenges in treatment efficacy. Stem cell therapy (SCT), an innovative field in regenerative medicine, holds immense promise for addressing these challenges. Stem cells, distinguished by their unique ability to differentiate into specialized cell types and self-renew, offer a valuable resource for tissue regeneration and healing. In this context, we have built a nonlinear ODE-based four dimensional mathematical model. This research article primarily aims to investigate the dynamic changes and interrelations of the cellular populations within the system during the progression of leprosy. The main focus throughout the research article is to predict the dissemination process of the disease following the transplantation of SCT. Specifically, our goal is to comprehend the disease dynamics involving M. leprae and Schwann cells due to the incorporation of stem cells through an impulsive manner. All analytical outcomes have been verified through numerical simulations and compared with existing clinical findings, ensuring the reliability and applicability of our novel research findings.