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Deep convolutional neural networks have shown remarkable performance on various computer vision tasks, and yet, they are susceptible to picking up spurious correlations from the training signal. So called `shortcuts' can occur during learning, for example, when there are specific frequencies present in the image data that correlate with the output predictions. Both high and low frequencies can be characteristic of the underlying noise distribution caused by the image acquisition rather than in relation to the task-relevant information about the image content. Models that learn features related to this characteristic noise will not generalize well to new data. In this work, we propose a simple yet effective training strategy, Frequency Dropout, to prevent convolutional neural networks from learning frequency-specific imaging features. We employ randomized filtering of feature maps during training which acts as a feature-level regularization. In this study, we consider common image processing filters such as Gaussian smoothing, Laplacian of Gaussian, and Gabor filtering. Our training strategy is model-agnostic and can be used for any computer vision task. We demonstrate the effectiveness of Frequency Dropout on a range of popular architectures and multiple tasks including image classification, domain adaptation, and semantic segmentation using both computer vision and medical imaging datasets. Our results suggest that the proposed approach does not only improve predictive accuracy but also improves robustness against domain shift.