Using density functional theory calculations, we have found an enhanced magneto-optical Kerr effect in Fe/insulator interfaces. The results of our study indicate that interfacial Fe atoms in the Fe films have a low-dimensional nature, which causes the following two effects: (i) The diagonal component σxx of the optical conductivity decreases dramatically because the hopping integral for electrons between Fe atoms is suppressed by the low dimensionality. (ii) The off-diagonal component σxy of the optical conductivity does not change at low photon energies, but it is enhanced at photon energies around 2 eV, where we obtain enhanced orbital magnetic moments and spin-orbit correlations for the interfacial Fe atoms. A large Kerr angle develops in proportion to the ratio σxy/σxx. Our findings indicate an efficient way to enhance the effect of spin-orbit coupling at metal/insulator interfaces without using heavy elements.