Single-cell analysis, or cytometry, is a ubiquitous tool in the biomedical sciences. Whereas most cytometers use fluorescent probes to ascertain the presence or absence of targeted molecules, biophysical parameters such as the cell density, refractive index, and viscosity are difficult to obtain. In this work, we combine two complementary techniques—quantitative phase imaging and Brillouin spectroscopy—into a label-free image cytometry platform capable of measuring more than a dozen biophysical properties of individual cells simultaneously. Using a geometric simplification linked to freshly plated cells, we can acquire the cellular diameter, volume, refractive index, mass density, non-aqueous mass, fluid volume, dry volume, the fractional water content of cells, both by mass and by volume, the Brillouin shift, Brillouin linewidth, longitudinal modulus, longitudinal viscosity, the loss modulus, and the loss tangent, all from a single acquisition, and with no assumptions of underlying parameters. Our methods are validated across three cell populations, including a control population of CHO-K1 cells, cells exposed to tubulin-disrupting nocodazole, and cells under hypoosmotic shock. Our system will unlock new avenues of research in biophysics, cell biology, and medicine.