The martian upper atmosphere could be strongly perturbed by the near collision with Comet C/2013 A1 (Siding Spring). Significant mass and energy will be deposited in the upper atmosphere of Mars if the comet coma is sufficiently dense. We predict that comet H₂O production rates larger than 10²⁸ molecules/s would produce temperature increases exceeding 30 K and the H density in the upper atmosphere will approximately double. The temperature perturbation will persist for several hours and the increased H density for tens of hours. Drag on orbiting spacecraft may increase by substantial factors, depending upon comet activity, because of the thermal perturbation to the atmosphere. Observation of these perturbations may provide insight into the thermal and chemical balances of the atmosphere.