Satellite hyperspectral remote sensing has gradually become an important means of Earth observation, but the existence of various types of noise seriously limits the application value of satellite hyperspectral images. With the continuous development of deep learning technology, breakthroughs have been made in improving hyperspectral image denoising algorithms based on supervised learning; however, these methods usually require a large number of clean/noisy training pairs, a target that is difficult to meet for real satellite hyperspectral imagery. In this paper, we propose a self-supervised learning-based algorithm, 3S-HSID, for denoising real satellite hyperspectral images without requiring external data support. The 3S-HSID framework can perform robust denoising of a single satellite hyperspectral image in all bands simultaneously. It first conducts a Bernoulli sampling of the input data, then uses the Bernoulli sampling results to construct the training pairs. Furthermore, the global spectral consistency and minimum local variance are used in the loss function to train the network. We use the training model to predict different Bernoulli sampling results, and the average of multiple predicted values is used as the denoising result. To prevent overfitting, we adopt a dropout strategy during training and testing. The results of denoising experiments on the simulated hyperspectral data show that the denoising performance of 3S-HSID is better than most state-of-the-art algorithms, especially in terms of maintaining the spectral characteristics of hyperspectral images. The denoising results for different types of real satellite hyperspectral data also demonstrate the reliability of the proposed method. The 3S-HSID framework provides a new technical means for real satellite hyperspectral image preprocessing.