The downwind configuration of wind turbines offers benefits regarding the blade-tower clearance, as during operation the blade primarily bends away from the tower. Consequently, the blades can be designed with lower stiffness. For tubular towers, however, a significant deficit of the wind speed in the tower wake occurs, resulting in fatigue-inducing vibrations. For this reason, full-height lattice towers are considered the preferred support structures for wind turbines with a downwind rotor. This work estimates the tower shadow excitation of a downwind rotor blade from a tubular tower. To this end, the blade of a commercial 6 MW downwind turbine is modelled with finite-elements. The tower wake is described on the basis of Madsen's model and for the unsteady aerodynamic interaction Küssner's function is adopted. At below- and above-rated wind conditions, the tower wake-induced vibrations are compared with the response of a blade of an equivalent upwind rotor, considering both the tip deflections and the root moments, the latter on the basis of damage-equivalent moments, to obtain an indication of the expected difference in fatigue damage. The downwind blade experiences vibrations with considerable larger amplitudes, especially in the out-of-plane direction. From the damage-equivalent moments it can be inferred that the blades of the downwind rotor encounter a much faster accumulation of fatigue damage.