The effective Lagrangian of QED coupled to dyons is calculated. The resulting generalization of the EulerHeisenberg Lagrangian contains nonlinear P-and T-noninvariant terms corresponding to the virtual pair creation of dyons. The corresponding P-and T-violating part of the matrix element for light-by-light scattering is considered. This effect induces an electric dipole moment for the electron, of order M Ϫ2 , where M is the dyon mass. The current limit on the electric dipole moment of the electron yields the lower dyon mass bound M Ͼ1 TeV. ͓S0556-2821͑97͒06109-2͔