Three-dimensional magnetophotonic crystals (3D-MPCs) are being postulated as appropriate platforms to tailor the magneto-optical spectral response of magnetic materials and to incorporate this functionality in a new generation of optical devices. By infiltrating self-assembled inverse opal structures with monodisperse nickel nanoparticles we have fabricated 3D-MPCs that show a sizable enhancement of the magneto-optical signal at frequencies around the stop-band edges of the photonic crystals. We have established a proper methodology to disentangle the intrinsic magneto-optical spectra from the nonmagnetic optical activity of the 3D-MPCs. The results of the optical and magneto-optical characterization are consistent with a homogeneous magnetic infiltration of the opal structure that gives rise to both a red-shift of the optical bandgap and a modification of the magneto-optical spectral response due to photonic bandgap effects. The results of our investigation demonstrate the potential of 3D-MPCs fabricated following the approach outlined here and offer opportunities to adapt the magneto-optical spectral response at optical frequencies by appropriate design of the opal structure or magnetic field strength.