In the pursuit of enhancing software reusability and developer productivity, code search has emerged as a key area, aimed at retrieving code snippets relevant to functionalities based on natural language queries. Despite significant progress in self-supervised code pre-training utilizing the vast amount of code data in repositories, existing methods have primarily focused on leveraging contrastive learning to align natural language with function-level code snippets. These studies have overlooked the abundance of fine-grained (such as block-level and statement-level) code snippets prevalent within the function-level code snippets, which results in suboptimal performance across all levels of granularity. To address this problem, we first construct a multi-granularity code search dataset called MGCodeSearchNet, which contains 536K+ pairs of natural language and code snippets. Subsequently, we introduce a novel Multi-Granularity Self-Supervised contrastive learning code Search framework (MGS$^{3}$}). First, MGS$^{3}$ features a Hierarchical Multi-Granularity Representation module (HMGR), which leverages syntactic structural relationships for hierarchical representation and aggregates fine-grained information into coarser-grained representations. Then, during the contrastive learning phase, we endeavor to construct positive samples of the same granularity for fine-grained code, and introduce in-function negative samples for fine-grained code. Finally, we conduct extensive experiments on code search benchmarks across various granularities, demonstrating that the framework exhibits outstanding performance in code search tasks of multiple granularities. These experiments also showcase its model-agnostic nature and compatibility with existing pre-trained code representation models.