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In this paper, we explore the problem of deep multi-view subspace clustering framework from an information-theoretic point of view. We extend the traditional information bottleneck principle to learn common information among different views in a self-supervised manner, and accordingly establish a new framework called Self-supervised Information Bottleneck based Multi-view Subspace Clustering (SIB-MSC). Inheriting the advantages from information bottleneck, SIB-MSC can learn a latent space for each view to capture common information among the latent representations of different views by removing superfluous information from the view itself while retaining sufficient information for the latent representations of other views. Actually, the latent representation of each view provides a kind of self-supervised signal for training the latent representations of other views. Moreover, SIB-MSC attempts to learn the other latent space for each view to capture the view-specific information by introducing mutual information based regularization terms, so as to further improve the performance of multi-view subspace clustering. To the best of our knowledge, this is the first work to explore information bottleneck for multi-view subspace clustering. Extensive experiments on real-world multi-view data demonstrate that our method achieves superior performance over the related state-of-the-art methods.