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We examine magnetorotationally driven supernovae as sources of r-process elements in the early Galaxy. On the basis of thermodynamic histories of tracer particles from a three-dimensional magnetohydrodynamical core-collapse supernova model with approximated neutrino transport, we perform nucleosynthesis calculations with and without considering the effects of neutrino absorption reactions on the electron fraction (Y-e) during post-processing. We find that the peak distribution of Y-e in the ejecta is shifted from similar to 0.15 to similar to 0.17 and broadened toward higher Y-e due to neutrino absorption. Nevertheless, in both cases, the second and third peaks of the solar r-process element distribution can be reproduced well. The rare progenitor configuration that was used here, characterized by a high rotation rate and a large magnetic field necessary for the formation of bipolar jets, could naturally provide a site for the strong r-process in agreement with observations of the early Galactic chemical evolution.