Supervised learning with a convolutional neural network is recognized as a powerful means of image restoration. However, most such methods have been designed for application to grayscale and/or color images; therefore, they have limited success when applied to hyperspectral image restoration. This is partially owing to large datasets being difficult to collect, and also the heavy computational load associated with the restoration of an image with many spectral bands. To address this difficulty, we propose a novel self-supervised learning strategy for application to hyperspectral image restoration. Our method automatically creates a training dataset from a single degraded image and trains a denoising network without any clear images. Another notable feature of our method is the use of a separable convolutional layer. We undertake experiments to prove that the use of a separable network allows us to acquire the prior of a hyperspectral image and to realize efficient restoration. We demonstrate the validity of our method through extensive experiments and show that our method has better characteristics than those that are currently regarded as state-of-the-art.