We investigate the optical response of an atomic Bose-Einstein condensate with a vortex lattice. We find that it is possible for the vortex lattice to act as a photonic crystal and create photonic band gaps, by enhancing the refractive index of the condensate via a quantum coherent scheme. If high enough index contrast between the vortex core and the atomic sample is achieved, a photonic band gap arises depending on the healing length and the lattice spacing. A wide range of experimentally accessible parameters are examined and band gaps in the visible region of the electromagnetic spectrum are found. We also show how directional band gaps can be used to directly measure the rotation frequency of the condensate.