We apply for the first time the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second-order correction (beyond the mean-field approximation) to the equation of state of symmetric nuclear matter with a zero-range effective interaction. The unphysical ultraviolet divergence generated at second order by the zero range of the interaction is properly removed by the regularization technique and the regularized equation of state (mean-field + second-order contributions) is adjusted to a reference equation of state. One of the main practical advantages of this procedure, with respect to a cutoff regularization, is to provide a unique set of parameters for the adjusted effective interaction. This occurs because the regularized second-order correction does not contain any cutoff dependence. The encouraging results found in this work indicate that such an elegant and rigorous technique to remove the divergent terms and to generate regularized effective interactions is likely to be applied in future in the framework of beyond mean-field models for finite nuclei.