We address the problem of data-driven image manipulation detection in the presence of an attacker with limited knowledge about the detector. Specifically, we assume that the attacker knows the architecture of the detector, the training data and the class of features V the detector can rely on. In order to get an advantage in his race of arms with the attacker, the analyst designs the detector by relying on a subset of features chosen at random in V. Given its ignorance about the exact feature set, the adversary attacks a version of the detector based on the entire feature set. In this way, the effectiveness of the attack diminishes since there is no guarantee that attacking a detector working in the full feature space will result in a successful attack against the reduced-feature detector. We theoretically prove that, thanks to random feature selection, the security of the detector increases significantly at the expense of a negligible loss of performance in the absence of attacks. We also provide an experimental validation of the proposed procedure by focusing on the detection of two specific kinds of image manipulations, namely adaptive histogram equalization and median filtering. The experiments confirm the gain in security at the expense of a negligible loss of performance in the absence of attacks.