We investigate the flux tube joining two equal and opposite electric charges using the dual Ginzburg-Landau model of superconductivity. The model is supplemented with an additional scalar field carrying a non-Abelian global symmetry, broken in the vortex cores. The presence of orientational moduli makes the flux tube non-Abelian. We perform a detailed study of the low-energy theory of this soliton. We also analyze the solution representing superconducting droplets in the presence of the monopole-antimonopole pair.