Understanding semantic information is an essential step in knowing what is being learned in both full-reference (FR) and no-reference (NR) image quality assessment (IQA) methods. However, especially for many severely distorted images, even if there is an undistorted image as a reference (FR-IQA), it is difficult to perceive the lost semantic and texture information of distorted images directly. In this paper, we propose a Mask Reference IQA (MR-IQA) method that masks specific patches of a distorted image and supplements missing patches with the reference image patches. In this way, our model only needs to input the reconstructed image for quality assessment. First, we design a mask generator to select the best candidate patches from reference images and supplement the lost semantic information in distorted images, thus providing more reference for quality assessment; in addition, the different masked patches imply different data augmentations, which favors model training and reduces overfitting. Second, we provide a Mask Reference Network (MRNet): the dedicated modules can prevent disturbances due to masked patches and help eliminate the patch discontinuity in the reconstructed image. Our method achieves state-of-the-art performances on the benchmark KADID-10k, LIVE and CSIQ datasets and has better generalization performance across datasets. The code and results are available in the supplementary material.