Color is a crucial visual cue readily exploited by Convolutional Neural Networks (CNNs) for object recognition. However, CNNs struggle if there is data imbalance between color variations introduced by accidental recording conditions. Color invariance addresses this issue but does so at the cost of removing all color information, which sacrifices discriminative power. In this paper, we propose Color Equivariant Convolutions (CEConvs), a novel deep learning building block that enables shape feature sharing across the color spectrum while retaining important color information. We extend the notion of equivariance from geometric to photometric transformations by incorporating parameter sharing over hue-shifts in a neural network. We demonstrate the benefits of CEConvs in terms of downstream performance to various tasks and improved robustness to color changes, including train-test distribution shifts. Our approach can be seamlessly integrated into existing architectures, such as ResNets, and offers a promising solution for addressing color-based domain shifts in CNNs.