Federated learning facilitates the collaborative learning of a global model across multiple distributed medical institutions without centralizing data. Nevertheless, the expensive cost of annotation on local clients remains an obstacle to effectively utilizing local data. To mitigate this issue, federated active learning methods suggest leveraging local and global model predictions to select a relatively small amount of informative local data for annotation. However, existing methods mainly focus on all local data sampled from the same domain, making them unreliable in realistic medical scenarios with domain shifts among different clients. In this paper, we make the first attempt to assess the informativeness of local data derived from diverse domains and propose a novel methodology termed Federated Evidential Active Learning (FEAL) to calibrate the data evaluation under domain shift. Specifically, we introduce a Dirichlet prior distribution in both local and global models to treat the prediction as a distribution over the probability simplex and capture both aleatoric and epistemic uncertainties by using the Dirichlet-based evidential model. Then we employ the epistemic uncertainty to calibrate the aleatoric uncertainty. Afterward, we design a diversity relaxation strategy to reduce data redundancy and maintain data diversity. Extensive experiments and analyses are conducted to show the superiority of FEAL over the state-of-the-art active learning methods and the efficiency of FEAL under the federated active learning framework.