Cellular therapies for burn wound healing, including the administration of mesenchymal stem or stromal cells (MSCs), have shown promising results. This review aims to provide an overview of the current administration methods in preclinical and clinical studies of bone-marrow-, adipose-tissue-, and umbilical-cord-derived MSCs for treating burn wounds. Relevant studies were identified through a literature search in PubMed and Embase and subjected to inclusion and exclusion criteria for eligibility. Additional relevant studies were identified through a manual search of reference lists. A total of sixty-nine studies were included in this review. Of the included studies, only five had clinical data from patients, one was a prospective case–control, three were case reports, and one was a case series. Administration methods used were local injection (41% in preclinical and 40% in clinical studies), cell-seeded scaffolds (35% and 20%), topical application (17% and 60%), and systemic injection (1% and 0%). There was great heterogeneity between the studies regarding experimental models, administration methods, and cell dosages. Local injection was the most common administration method in animal studies, while topical application was used in most clinical reports. The best delivery method of MSCs in burn wounds is yet to be identified. Although the potential of MSC treatment for burn wounds is promising, future research should focus on examining the effect and scalability of such therapy in clinical trials.