In recent times, monocular depth estimation (MDE) has experienced significant advancements in performance, largely attributed to the integration of innovative architectures, i.e., convolutional neural networks (CNNs) and Transformers. Nevertheless, the susceptibility of these models to adversarial attacks has emerged as a noteworthy concern, especially in domains where safety and security are paramount. This concern holds particular weight for MDE due to its critical role in applications like autonomous driving and robotic navigation, where accurate scene understanding is pivotal. To assess the vulnerability of CNN-based depth prediction methods, recent work tries to design adversarial patches against MDE. However, the existing approaches fall short of inducing a comprehensive and substantially disruptive impact on the vision system. Instead, their influence is partial and confined to specific local areas. These methods lead to erroneous depth predictions only within the overlapping region with the input image, without considering the characteristics of the target object, such as its size, shape, and position. In this paper, we introduce a novel adversarial patch named APARATE. This patch possesses the ability to selectively undermine MDE in two distinct ways: by distorting the estimated distances or by creating the illusion of an object disappearing from the perspective of the autonomous system. Notably, APARATE is designed to be sensitive to the shape and scale of the target object, and its influence extends beyond immediate proximity. APARATE, results in a mean depth estimation error surpassing $0.5$, significantly impacting as much as $99\%$ of the targeted region when applied to CNN-based MDE models. Furthermore, it yields a significant error of $0.34$ and exerts substantial influence over $94\%$ of the target region in the context of Transformer-based MDE.