Skeletal muscle is a highly organized and regenerative tissue that maintains its homeostasis primarily by activation and differentiation of muscle stem cells. Mimicking an in vitro skeletal muscle differentiation program that contains self-renewing adult muscle stem cells and aligned myotubes has been challenging. Here, we set out to engineer a biomimetic skeletal muscle construct that can self-regenerate and produce aligned myotubes using induced myogenic progenitor cells (iMPCs), a heterogeneous culture consisting of skeletal muscle stem, progenitor and differentiated cells. Utilizing electrospinning, we fabricated polycaprolactone (PCL) substrates that enabled iMPC-differentiation into aligned myotubes by controlling PCL fiber orientation. Newly-conceived constructs contained highly organized multinucleated myotubes in conjunction with self-renewing muscle stem cells, whose differentiation capacity was augmented by Matrigel supplementation. Additionally, we demonstrate using single cell RNA-sequencing (scRNA-seq) that iMPC-derived constructs faithfully recapitulate a step-wise myogenic differentiation program. Notably, when the constructs were subjected to a damaging myonecrotic agent, self-renewing muscle stem cells rapidly differentiated into aligned myotubes, akin to skeletal muscle repair in vivo. Taken together, we report on a novel in vitro system that mirrors myogenic regeneration and muscle fiber alignment, and can serve as a platform to study myogenesis, model muscular dystrophies or perform drug screens.