We show that the electroweak monopole can be regularized with a non-vacuum electromagnetic permittivity. This allows us to set a new BPS bound for the monopole mass, which implies that the mass may not be smaller than 2.98 TeV, more probably 3.75 TeV. We demonstrate that the same method can also regularize the Dirac monopole, which enhances the possibility to construct the Dirac monopole of mass of a few hundred meV in condensed matters. We discuss the physical implications of our result.Keywords: Cho-Maison monopole, finite energy electroweak monopole, regularization of the electroweak monopole by electric charge renormalization, BPS electroweak monopole, BPS energy bound of electroweak monopole, lower bound of electroweak monopole mass, regularized Dirac monopole by vacuum polarization * Electronic address: zhangpm5@mail.sysu.edu.cn † Electronic address: zoulp@impcas.ac.cn ‡ Electronic address: ymcho0416@gmail.com correct. This is because the unification inevitably makes the electromagnetic U(1) non-trivial [7,8].