Adversarial example detection is known to be an effective adversarial defense method. Black-box attack, which is a more realistic threat and has led to various black-box adversarial training-based defense methods, however, does not attract considerable attention in adversarial example detection. In this paper, we fill this gap by positioning the problem of black-box adversarial example detection (BAD). Data analysis under the introduced BAD settings demonstrates (1) the incapability of existing detectors in addressing the black-box scenario and (2) the potential of exploring BAD solutions from a data perspective. To tackle the BAD problem, we propose a data reconstruction-based adversarial example detection method. Specifically, we use variational auto-encoder (VAE) to capture both pixel and frequency representations of normal examples. Then we use reconstruction error to detect adversarial examples. Compared with existing detection methods, the proposed method achieves substantially better detection performance in BAD, which helps promote the deployment of adversarial example detection-based defense solutions in real-world models.