The evolution of the magnetic structure for an inverse opal-like structure under an applied magnetic field is studied by small-angle neutron scattering. The samples were produced by filling the voids of an artificial opal film with Co. It is shown that the local configuration of magnetization is inhomogeneous over the basic element of the inverse opal-like lattice structure (IOLS) but follows its periodicity. Applying the “ice-rule” concept to the structure, we describe the local magnetization of this ferromagnetic three-dimensional lattice. We have developed a model of the remagnetization process predicting the occurrence of an unusual perpendicular component of the magnetization in the IOLS which is defined only by the direction and strength of the applied magnetic field.