The dynamics of nanosystems in solution contains a wealth of information with relevance for diverse fields ranging from materials science to biology and biomedical applications. When nanosystems are marked with fluorophores or strong scatterers, it is possible to track their position and reveal internal motion with high spatial and temporal resolution. However, markers can be toxic, expensive, or change the object's intrinsic properties. Here, we simultaneously measure dispersive frequency shifts of three transversal modes of a high-finesse microcavity to obtain the three-dimensional path of unlabeled SiO2 nanospheres with 300μs temporal and down to 8nm spatial resolution. This allows us to quantitatively determine properties such as the polarizability, hydrodynamic radius, and effective refractive index. The fiber-based cavity is integrated in a direct-laser-written microfluidic device that enables the precise control of the fluid with ultra-small sample volumes. Our approach enables quantitative nanomaterial characterization and the analysis of biomolecular motion at high bandwidth.