Magnetic moments near zigzag edges in graphene allow complex nanostructures with customized spin properties to be realized. However, computational costs restrict theoretical investigations to small or perfectly periodic structures. Here, we demonstrate that a machine-learning approach, using only geometric input, can accurately estimate magnetic moment profiles, allowing arbitrarily large and disordered systems to be quickly simulated. Excellent agreement is found with mean-field Hubbard calculations, and important electronic, magnetic, and transport properties are reproduced using the estimated profiles. This approach allows the magnetic moments of experimental-scale systems to be quickly and accurately predicted, and will speed up the identification of promising geometries for spintronic applications. While machine-learning approaches to many-body interactions have largely been limited to exact solutions of complex models at very small scales, this Letter establishes that they can be successfully applied at very large scales at mean-field levels of accuracy.