Prevalent techniques in label-free linear optical microscopy are either confined to imaging in two dimensions or rely on scanning, both of which restrict their applications in imaging subtle biological dynamics. In this paper, we present the theoretical basis along with demonstrations supporting that full-field spectral-domain interferometry can be used for imaging samples in 3D with no moving parts in a single shot. Consequently, we propose a novel optical imaging modality that combines low-coherence interferometry with hyperspectral imaging using a light-emitting diode and an image mapping spectrometer, called Snapshot optical coherence microscopy (OCM). Having first proved the feasibility of Snapshot OCM through theoretical modeling and a comprehensive simulation, we demonstrate an implementation of the technique using off-the-shelf components capable of capturing an entire volume in 5 ms. The performance of Snapshot OCM, when imaging optical targets, shows its capability to axially localize and section images over an axial range of ±10 µm, while maintaining a transverse resolution of 0.8 µm, an axial resolution of 1.4 µm, and a sensitivity of up to 80 dB. Additionally, its performance in imaging weakly scattering live cells shows its capability to not only localize the cells in a densely populated culture but also to generate detailed phase profiles of the structures at each depth for long durations. Consolidating the advantages of several widespread optical microscopy modalities, Snapshot OCM has the potential to be a versatile imaging technique for a broad range of applications.