Treatment of severe burn wounds presents a daunting medical challenge, and novel approaches promoting healing and reducing scarring are highly desirable. The application of mesenchymal stem/stromal cells (MSCs) has been suggested as a novel treatment. In this paper, we present systematic reviews of pre-clinical and clinical studies of MSC therapy for second- or third-degree thermal burn wounds. Following the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines, the PubMed and Embase databases were searched, and interventional studies of MSC therapy using rodent models (21 studies) or human burn patients (three studies) were included in the pre-clinical and clinical reviews, respectively, where both overall outcome and wound-healing-phase-specific methodologies and effects were assessed. The pre-clinical studies demonstrated a promising effect of the application of MSCs on several wound healing phases. The clinical studies also suggested that the MSC treatment was beneficial, particularly in the remodeling phase. However, the limited number of studies, their lack of homogeneity in study design, relatively high risk of bias, lack of reporting on mode of action (MOA), and discontinuity of evidence restrict the strength of these findings. This comprehensive review presents an overview of available methodologies to assess the MOA of MSC treatment for distinct wound healing phases. Furthermore, it includes a set of recommendations for the design of high-quality clinical studies that can determine the efficacy of MSCs as a therapy for burn wounds.