Recent studies unveil the vulnerabilities of deep ranking models, where an imperceptible perturbation can trigger dramatic changes in the ranking result. While previous attempts focus on manipulating absolute ranks of certain candidates, the possibility of adjusting their relative order remains under-explored. In this paper, we formulate a new adversarial attack against deep ranking systems, i.e., the Order Attack, which covertly alters the relative order among a selected set of candidates according to an attacker-specified permutation, with limited interference to other unrelated candidates. Specifically, it is formulated as a triplet-style loss imposing an inequality chain reflecting the specified permutation. However, direct optimization of such white-box objective is infeasible in a real-world attack scenario due to various black-box limitations. To cope with them, we propose a Short-range Ranking Correlation metric as a surrogate objective for black-box Order Attack to approximate the white-box method. The Order Attack is evaluated on the Fashion-MNIST and Stanford-Online-Products datasets under both white-box and black-box threat models. The black-box attack is also successfully implemented on a major e-commerce platform. Comprehensive experimental evaluations demonstrate the effectiveness of the proposed methods, revealing a new type of ranking model vulnerability.