Automatic query reformulation is a widely used technology to enhance code search results, by formulating as a machine translation problem of rewriting a query into a more comprehensive alternative. While showing promising results, it typically requires a large parallel corpus of query pairs (i.e., the original query and a reformulated query) that are confidential and unpublished by online code search engines. This restricts its practicality in software development. In this paper, we propose SSQR, a self-supervised query reformulation method that does not rely on any parallel query corpus. Inspired by pre-trained models, SSQR treats query reformulation as a masked language modeling task over a large-scale unlabelled corpus of queries. SSQR extends T5 (a sequence-to-sequence model based on Transformer) with a new pre-training objective named corrupted query completion (CQC), which randomly masks words from a complete query and asks T5 to predict the masked content. Then, for a given query to be reformulated, SSQR enumerates candidate positions to be expanded and employs the pre-trained T5 model to generate the content to fill the spans. Finally, SSQR selects expansions that have the most information gain. Our evaluation shows that SSQR significantly outperforms unsupervised baselines and gains competitive performance over supervised methods.