Burns are a major threat to public health and the economy due to their costly and laborious treatment and high susceptibility to infection. Efforts have been made recently to investigate natural bioactive compounds with potential use in wound healing. The importance lies in the capacities that these compounds could possess both in infection control by common and resistant microorganisms, as well as in the regeneration of the affected tissues, having in both cases low adverse effects. However, some bioactive molecules are chemically unstable, poorly soluble, and susceptible to oxidative degradation or have low bioavailability. Therefore, developing new technologies for an efficient treatment of wound healing poses a real challenge. In this context, electrospun nanofibers have gained increasing research interest because bioactive molecules can be easily loaded within the nanofiber, resulting in optimal burst control and enhanced drug stability. Additionally, the nanofibers can mimic the extracellular collagen matrix, providing a suitable highly porous structural support for growing cells that facilitate and accelerate skin burns healing. This review gives an overview of the current state of electrospun fibers loaded with natural bioactive compounds as a biomedical system for skin burn treatment.