Single crystal X-ray and synchrotron X-ray powder diffraction have been used to probe the structure of Ba3NaIr2O9 from 300 K down to 20 K. Ba3NaIr2O9 is found to undergo a structural transition from hexagonal symmetry, P63/mmc, at ambient temperature to monoclinic symmetry, C2/c, at low temperature. The evolution of the unit cell volume upon cooling is indicative of a higher order structural transition, and the symmetry breaking becomes apparent as the temperature is decreased. The low temperature monoclinic structure of Ba3NaIr2O9 contains strongly distorted [NaO6] and [IrO6] octahedra in comparison to the room temperature hexagonal structure.