We investigate the spatial variation of the demagnetizing field for uniformly magnetized, cylindrical samples using a recently developed Fourier space approach. We show that the demagnetizing response of the sample leads to a position dependence of the magnetic field, which varies most strongly near the radial boundary of the cylinder. Furthermore, we demonstrate that the demagnetizing field leads to a subsequent broadening of the field distribution, as experienced by the muons implanted in the sample, with a characteristic shape including a low field tail and a sharp high-field cutoff. We present a detailed study of this field broadening as a function of the aspect ratio of the cylinder and find that it is significant and largest for aspect ratios typical for cylindrical samples grown in mirror furnaces. We identify two strategies to minimize this broadening: adding a degrader so that muons implant closer to the surface of the sample and using a circular mask to stop muons from implanting near the radial edge. This could help identify whether an experimentally observed broadening is caused by the demagnetization response or the intrinsic properties of the sample.