Training a convolutional neural network (CNN) to detect infrared small targets in a fully supervised manner has gained remarkable research interests in recent years, but is highly labor expensive since a large number of per-pixel annotations are required. To handle this problem, in this paper, we make the first attempt to achieve infrared small target detection with point-level supervision. Interestingly, during the training phase supervised by point labels, we discover that CNNs first learn to segment a cluster of pixels near the targets, and then gradually converge to predict groundtruth point labels. Motivated by this “mapping degeneration” phenomenon, we propose a label evolution framework named label evolution with single point supervision (LESPS) to progressively expand the point label by leveraging the intermediate predictions of CNNs. In this way, the network predictions can finally approximate the updated pseudo labels, and a pixel-level target mask can be obtained to train CNNs in an end-to-end manner. We conduct extensive experiments with insightful visualizations to validate the effectiveness of our method. Experimental results show that CNNs equipped with LESPS can well recover the target masks from corresponding point labels, and can achieve over 70% and 95% of their fully supervised performance in terms of pixel-level intersection over union (IoU) and object-level probability of detection (Pd), respectively. Code is available at https://github.com/XinyiYing/LESPS.