A constraint between the photon mass and the parameters gamma (the deflection parameter determined by experimentalists) and nu (the photon frequency) is found by judiciously combining General Relativity and Massive QED. By adopting this scenario and by considering as inputs the most recent measurements of the solar gravitational deflection of radio waves obtained by means of the Very Long Baseline Interferometry, gravitational upper bounds on the photon mass are estimated. (C) 2010 Elsevier B.V. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)