Hyperspectral image (HSI) denoising is an ill-posed inverse problem. The underlying physical model is always important to tackle this problem, which is unfortunately ignored by most of the current deep learning (DL)-based methods, producing poor denoising performance. To address this issue, this paper introduces an end-to-end model aided nonlocal neural network (MAC-Net) which simultaneously takes the spectral low-rank model and spatial deep prior into account for HSI noise reduction. Specifically, motivated by the success of the spectral low-rank model in depicting the strong spectral correlations and the nonlocal similarity prior in capturing spatial long-range dependencies, we first build a spectral low-rank model and then integrate a nonlocal U-Net into the model. In this way, we obtain a hybrid model-based and DL-based HSI denoising method where the spatial local and nonlocal multi-scale and spectral low-rank structures are effectively exploited. After that, we cast the optimization and denoising procedure of the hybrid method as a forward process of a neural network and introduce a set of learnable modules to yield our MAC-Net. Compared with traditional model-based methods, our MAC-Net overcomes the difficulties of accurate modeling thanks to the strong learning and representation ability of DL. Unlike most “black-box” DL-based methods, the spectral low-rank model is beneficial to increase the generalization ability of the network and decrease the requirement of training samples. Experimental results on the natural and remote sensing HSIs show that MAC-Net achieves state-of-the-art performance over both model-based and DL-based methods. The source code and data of this article will be made publicly available at https://github.com/bearshng/mac-net for reproducible research.