In a semiconductor heterostructure, the Coulomb interaction is responsible for the electric current drag between two 2D electron gases across an electron impenetrable insulator. For two metallic layers separated by a ferromagnetic insulator (FI) layer, the electric current drag can be mediated by a nonequilibrium magnon current of the FI. We determine the drag current by using the semiclassical Boltzmann approach with proper boundary conditions of electrons and magnons at the metal-FI interface.