Muscular dystrophies are approximately 50 devastating, untreatable monogenic diseases leading to progressive muscle degeneration and atrophy. Gene correction of transplantable cells using CRISPR/Cas9-based tools is a realistic scenario for autologous cell replacement therapies to restore organ function in many genetic disorders. However, muscle stem cells have so far lagged behind due to the absence of methods to isolate and propagate them and their susceptibility to extensive ex vivo manipulations. Here, we show that mRNA-based delivery of SpCas9 and an adenine base editor results in up to >90% efficient genome editing in human muscle stem cells from many donors regardless of age and gender and without any enrichment step. Using NCAM1 as an endogenous reporter locus expressed by all muscle stem cells and whose knockout does not affect cell fitness, we show that cells edited with mRNA fully retain their myogenic marker signature, proliferation capacity, and functional attributes. Moreover, mRNA-based delivery of a base editor led to the highly efficient repair of a muscular dystrophy-causing SGCA mutation in a single selection-free step. In summary, our work establishes mRNA-mediated delivery of CRISPR/Cas9-based tools as a promising and universal approach for taking gene edited muscle stem cells into clinical application to treat muscle disease.