We demonstrate theoretically that, when quantum light interacts with massless Dirac fermions on the surface of a three-dimensional topological insulator, the elementary excitation spectrum depends on the polarizations of quantum light. Linear-polarized light cannot open a gap and leads to an anisotropic Dirac cone, but circular-polarized light can induce a mass term and the sign of mass is determined by the helicity of light. The effects due to quantum fluctuations are also discussed.