The mechanical properties of the nucleus are closely related to many cellular functions; thus, measuring nuclear mechanical properties is crucial to our understanding of cell biomechanics and could lead to intrinsic biophysical contrast mechanisms to classify cells. Although many technologies have been developed to characterize cell stiffness, they generally require contact with the cell and thus cannot provide direct information on nuclear mechanical properties. In this work, we developed a flow cytometry technique based on an all-optical measurement to measure nuclear mechanical properties by integrating Brillouin spectroscopy with microfluidics. Brillouin spectroscopy probes the mechanical properties of material via light scattering, so it is inherently label-free, non-contact, and non-invasive. Using a measuring beam spot of submicron size, we can measure several regions within each cell as they flow, which enables us to classify cell populations based on their nuclear mechanical signatures at a throughput of ~200 cells per hour. We show that Brillouin cytometry has sufficient sensitivity to detect physiologically-relevant changes in nuclear stiffness by probing the effect of drug-induced chromatin decondensation.