Monocular depth estimation (MDE) has advanced significantly, primarily through the integration of convolutional neural networks (CNNs) and more recently, Transformers. However, concerns about their susceptibility to adversarial attacks have emerged, especially in safety-critical domains like autonomous driving and robotic navigation. Existing approaches for assessing CNN-based depth prediction methods have fallen short in inducing comprehensive disruptions to the vision system, often limited to specific local areas. In this paper, we introduce SSAP (Shape-Sensitive Adversarial Patch), a novel approach designed to comprehensively disrupt monocular depth estimation (MDE) in autonomous navigation applications. Our patch is crafted to selectively undermine MDE in two distinct ways: by distorting estimated distances or by creating the illusion of an object disappearing from the system's perspective. Notably, our patch is shape-sensitive, meaning it considers the specific shape and scale of the target object, thereby extending its influence beyond immediate proximity. Furthermore, our patch is trained to effectively address different scales and distances from the camera. Experimental results demonstrate that our approach induces a mean depth estimation error surpassing 0.5, impacting up to 99% of the targeted region for CNN-based MDE models. Additionally, we investigate the vulnerability of Transformer-based MDE models to patch-based attacks, revealing that SSAP yields a significant error of 0.59 and exerts substantial influence over 99% of the target region on these models.