Volumetric reconstruction of label-free living cells from non-destructive optical microscopic images reveals cellular metabolism in native environments. However, current optical tomography techniques require hundreds of 2D images to reconstruct a 3D volume, hindering them from intravital imaging of biological samples undergoing rapid dynamics. This poses a challenge of reconstructing the entire volume of semi-transparent biological samples from sparse views due to the restricted viewing angles of microscopes and the limited number of measurements. In this work, we develop Neural Volumetric Prior (NVP) for high-fidelity volumetric reconstruction of semi-transparent biological samples from sparse-view microscopic images. NVP integrates explicit and implicit neural representations and incorporates the physical prior of diffractive optics. We validate NVP on both simulated data and experimentally captured microscopic images. Compared to previous methods, NVP significantly reduces the required number of images by nearly 50-fold and processing time by 3-fold while maintaining state-of-the-art performance.NVP is the first technique to enable volumetric reconstruction of label-free biological samples from sparse-view microscopic images, paving the way for real-time 3D imaging of dynamically changing biological samples.