Deep learning has achieved significant success in diffusion MRI (dMRI) computing. However, most deep learning-based dMRI methods heavily rely on supervised learning, which requires large-scale labeled datasets that are difficult to obtain. Recently, Masked AutoEncoder (MAE) has gained popularity in computer vision for its ability to leverage unlabeled data, yet its potential has not yet been fully explored in dMRI. To fill this gap, we propose the first MAE-based self-supervised learning framework, called DMAE, for representation learning of dMRI data. In DMAE, we first create dMRI patches using a deliberately designed tube q-space masking strategy, which adapts well to the unique q-space characteristics of dMRI data. We then encode the patches into a latent space for pre-training to learn high-level semantic representations. During the fine-tuning stage, we design a task-specific decoder and incorporate the decoder with the pre-trained encoder to achieve superior performance in downstream tasks. Extensive quantitative and qualitative results demonstrate the superiority of our framework over the state-of-the-art self-supervised learning approaches.