Metagenomics has led to significant advances in many fields. Metagenomic analysis commonly involves the key tasks of determining the species present in a sample and their relative abundances. These tasks require searching large metagenomic databases. Metagenomic analysis suffers from significant data movement overhead due to moving large amounts of low-reuse data from the storage system. In-storage processing can be a fundamental solution for reducing this overhead. However, designing an in-storage processing system for metagenomics is challenging because existing approaches to metagenomic analysis cannot be directly implemented in storage effectively due to the hardware limitations of modern SSDs. We propose MegIS, the first in-storage processing system designed to significantly reduce the data movement overhead of the end-to-end metagenomic analysis pipeline. MegIS is enabled by our lightweight design that effectively leverages and orchestrates processing inside and outside the storage system. We address in-storage processing challenges for metagenomics via specialized and efficient 1) task partitioning, 2) data/computation flow coordination, 3) storage technology-aware algorithmic optimizations, 4) data mapping, and 5) lightweight in-storage accelerators. MegIS's design is flexible, capable of supporting different types of metagenomic input datasets, and can be integrated into various metagenomic analysis pipelines. Our evaluation shows that MegIS outperforms the state-of-the-art performance- and accuracy-optimized software metagenomic tools by 2.7$\times$-37.2$\times$ and 6.9$\times$-100.2$\times$, respectively, while matching the accuracy of the accuracy-optimized tool. MegIS achieves 1.5$\times$-5.1$\times$ speedup compared to the state-of-the-art metagenomic hardware-accelerated (using processing-in-memory) tool, while achieving significantly higher accuracy.