Diabetic retinopathy (DR) is a leading cause of vision loss in the world and numerous cutting-edge works have built powerful deep neural networks (DNNs) to automatically classify the DR cases via the retinal fundus images (RFIs). However, RFIs are usually affected by the widely existing camera exposure while the robustness of DNNs to the exposure is rarely explored. In this paper, we study this problem from the viewpoint of adversarial attack and identify a totally new task, i.e., adversarial exposure attack generating adversarial images by tuning image exposure to mislead the DNNs with significantly high transferability. To this end, we first implement a straightforward method, i.e., multiplicative-perturbation-based exposure attack, and reveal the big challenges of this new task. Then, to make the adversarial image naturalness, we propose the adversarial bracketed exposure fusion that regards the exposure attack as an element-wise bracketed exposure fusion problem in the Laplacian-pyramid space. Moreover, to realize high transferability, we further propose the convolutional bracketed exposure fusion where the element-wise multiplicative operation is extended to the convolution. We validate our method on the real public DR dataset with the advanced DNNs, e.g., ResNet50, MobileNet, and EfficientNet, showing our method can achieve high image quality and success rate of the transfer attack. Our method reveals the potential threats to the DNN-based DR automated diagnosis and can definitely benefit the development of exposure-robust automated DR diagnosis method in the future.