We study the dimensional reduction for a (3 + 1)-dimensional Lorentz Violating Lagrangian in the matter and gauge sectors in a Supersymmetric scenario. We thus obtain an effective model for photons induced by the effects of supersymmetry in our framework with Lorentz-symmetry violating. This model is discussed in connection with the attainment of a static potential between charged particles. Our calculation is done within the framework of the gauge-invariant, but pathdependent variable formalism. We thus find that the interaction energy displays a screening part, encoded by Bessel functions, and a linear confining potential.