The Brain Imaging Data Structure (BIDS) is a specification for organizing, sharing, and archiving neuroimaging data and metadata in a reusable way. First developed for magnetic resonance imaging (MRI) datasets, the community-led specification evolved rapidly to include other modalities such as magnetoencephalography, positron emission tomography, and quantitative MRI (qMRI). In this work, we present an extension to BIDS for microscopy imaging data, along with example datasets. Microscopy-BIDS supports common imaging methods, including 2D/3D, ex/in vivo, micro-CT, and optical and electron microscopy. Microscopy-BIDS also includes comprehensible metadata definitions for hardware, image acquisition, and sample properties. This extension will facilitate future harmonization efforts in the context of multi-modal, multi-scale imaging such as the characterization of tissue microstructure with qMRI.