The higher order curvature corrections in Einstein-Gauss-Bonnet gravity play a significant role in the dynamics of gravitational collapse. We extend the gravitational collapse of radiating shells of matter in Einstein-Gauss-Bonnet gravity to higher dimensions, in the context of the cosmic censorship conjecture. In five dimensions the final collapse terminates with the formation of an extended and weak conical, naked singularity in the central region. For dimensions N >5 , we determine that collapse terminates with a strong curvature singularity which may or may not be naked. Cosmic censorship is affected by higher-order curvature corrections. A comparison with the higher-dimensional general relativity counterpart is also given, where the dynamics are affected by the higher dimensions.