In this paper, we propose a privacy-preserving image classification method that is based on the combined use of encrypted images and the vision transformer (ViT). The proposed method allows us not only to apply images without visual information to ViT models for both training and testing but to also maintain a high classification accuracy. ViT utilizes patch embedding and position embedding for image patches, so this architecture is shown to reduce the influence of block-wise image transformation. In an experiment, the proposed method for privacy-preserving image classification is demonstrated to outperform state-of-the-art methods in terms of classification accuracy and robustness against various attacks.