Federated learning enables multiple users to build a joint model by sharing their model updates (gradients), while their raw data remains local on their devices. In contrast to the common belief that this provides privacy benefits, we here add to the very recent results on privacy risks when sharing gradients. Specifically, we investigate Label Leakage from Gradients (LLG), a novel attack to extract the labels of the users' training data from their shared gradients. The attack exploits the direction and magnitude of gradients to determine the presence or absence of any label. LLG is simple yet effective, capable of leaking potential sensitive information represented by labels, and scales well to arbitrary batch sizes and multiple classes. We mathematically and empirically demonstrate the validity of the attack under different settings. Moreover, empirical results show that LLG successfully extracts labels with high accuracy at the early stages of model training. We also discuss different defense mechanisms against such leakage. Our findings suggest that gradient compression is a practical technique to mitigate the attack.