Few-shot hyperspectral image classification aims to develop the ability of classifying image pixels by using relatively few labeled pixels per class. However, due to the inaccuracy of the localization system and the bias of the ground survey, the potential noisy labels in the training data pose a very significant challenge to few-shot hyperspectral image classification. To solve this problem, this paper proposes a weighted contrastive prototype network (WCPN) for few-shot hyperspectral image classification with noisy labels. WCPN first utilizes a similarity metric to generate the weights of the samples from the same classes, and applies them to calibrate the class prototypes of support and query sets. Then the weighted prototype network will minimize the distance between features and prototypes to train the network. WCPN also incorporates a weighted contrastive regularization function that uses the sample weights as gates to filter the fake positive samples whose labels are incorrect to further improve the discriminative power of the prototypes. We conduct experiments on multiple hyperspectral image datasets with artificially generated noisy labels, and the results show that the WCPN has excellent performance that can sufficiently mitigate the impact of noisy labels.