Recent advances in nanotechnology and biomaterials engineering have enabled the development of next-generation nanofibrous wound dressings that more closely mimic the architecture of the extracellular matrix and provide an active microenvironment for tissue repair. In recent years, increasing attention has been directed toward integrating natural and synthetic polymeric nanofibers with bio-derived porous nanomaterials, particularly metal–organic frameworks (MOFs), to achieve multifunctional wound dressings. Such hybrid systems have demonstrated the potential to simultaneously promote hemostasis, modulate inflammation, control infection, and accelerate tissue regeneration. Despite encouraging preclinical outcomes, several challenges hinder clinical translation. A critical assessment of the existing literature reveals these challenges. These include substantial variability in material composition and fabrication strategies, a lack of standardized evaluation models, and ongoing concerns regarding long-term biocompatibility and metal ion release. Moreover, differences in wound models and assessment endpoints across studies complicate direct comparison of reported outcomes. This review provides a critical overview of recent developments in nanofibrous wound dressings incorporating MOFs, with particular emphasis on their biological mechanisms of action, therapeutic advantages, and current limitations. By highlighting existing knowledge gaps and unresolved safety and translational issues, this article aims to clarify future research directions and support the rational design of clinically viable nanofibrous wound dressing platforms.