Deep neural networks (DNNs) have proven to be powerful predictors and are widely used for various tasks. Credible uncertainty estimation of their predictions, however, is crucial for their deployment in many risk-sensitive applications. In this paper we present a novel and simple attack, which unlike adversarial attacks, does not cause incorrect predictions but instead cripples the network's capacity for uncertainty estimation. The result is that after the attack, the DNN is more confident of its incorrect predictions than about its correct ones without having its accuracy reduced. We present two versions of the attack. The first scenario focuses on a black-box regime (where the attacker has no knowledge of the target network) and the second scenario attacks a white-box setting. The proposed attack is only required to be of minuscule magnitude for its perturbations to cause severe uncertainty estimation damage, with larger magnitudes resulting in completely unusable uncertainty estimations. We demonstrate successful attacks on three of the most popular uncertainty estimation methods: the vanilla softmax score, Deep Ensembles and MC-Dropout. Additionally, we show an attack on SelectiveNet, the selective classification architecture. We test the proposed attack on several contemporary architectures such as MobileNetV2 and EfficientNetB0, all trained to classify ImageNet.