An infodemic refers to an enormous amount of true information and misinformation disseminated during a disease outbreak. Detecting misinformation at the early stage of an infodemic is key to reduce its harm to public health. An early stage infodemic is characterized by a large volume of unlabeled information concerning a disease. As a result, conventional misinformation detection methods are not suitable for this misinformation detection task because they rely on labeled information in the infodemic domain to train their models. To address this limitation, state-of-the-art methods learn their models using labeled information in other domains to detect misinformation in the infodemic domain. The efficacy of these methods depends on their ability to mitigate both covariate shift (i.e., differences in feature distributions) and concept shift (i.e., differences in labeling patterns) between the infodemic domain and the domains from which they leverage labeled information. However, these methods focus on mitigating covariate shift but overlook concept shift, rendering them less effective for the task. In response, we theoretically show the necessity of tackling both covariate and concept shifts as well as how to operationalize each of them. Built on the theoretical analysis, we develop a novel misinformation detection method that addresses both covariate and concept shifts. Using real-world datasets, we conduct extensive empirical evaluations to demonstrate the superior performance of our method over state-of-the-art misinformation detection methods as well as prevalent domain adaptation methods that can be tailored to solve the misinformation detection task.