The effective action of the recently proposed vector Galileon theory is considered. Using the background field method, we obtain the one-loop correction to the propagator of the Proca field from vector Galileon self-interactions. Contrary to the so-called scalar Galileon interactions, the two-point function of the vector field gets renormalized at the one-loop level, indicating that there is no nonrenormalization theorem in the vector Galileon theory. Using dimensional regularization, we remove the divergences and obtain the counterterms of the theory. The finite term is analytically calculated, which modifies the propagator and the mass term and generates some new terms also.