Computer-aided assessment of physical rehabilitation entails evaluation of patient performance in completing prescribed rehabilitation exercises, by processing movement data captured with a sensory system. Despite the essential role of rehabilitation assessment toward improved rehabilitation outcomes and reduced healthcare costs, existing approaches for computeraided monitoring and evaluation of patient performance lack versatility, robustness, and practical relevance. In this paper, we propose a deep learning-based framework for automated assessment of the quality of physical rehabilitation exercises. The main components of the framework are metrics for quantifying movement performance, scoring functions for mapping the performance metrics into numerical scores of movement quality, and deep neural network models for regressing quality scores of input movements via supervised learning. A performance metric based on the log-likelihood of a Gaussian mixture model used for encoding low-dimensional data representation obtained with a deep autoencoder network, is proposed in the paper. Multiple deep network architectures are repurposed for the task in hand and are validated by using a dataset of rehabilitation exercises. To the best of our knowledge, this is the first work that implements deep neural networks for the assessment of rehabilitation performance.