Volumetric, sub-micron to micron level resolution imaging is necessary to assay phenotypes or characteristics at the sub-cellular/organelle scale. However, three-dimensional fluorescence imaging of cells is typically low throughput or compromises on the achievable resolution in space and time. Here, we capitalise on the flow control capabilities of microfluidics and combine it with microoptics to integrate light-sheet based imaging directly into a microfluidic chip. Our optofluidic system flows suspended cells through a sub-micrometer thick light-sheet formed using micro-optical components that are cast directly in polydimethylsiloxane (PDMS). This design ensures accurate alignment, drift-free operation, and easy integration with conventional microfluidics, while providing sufficient spatial resolution, optical sectioning and volumetric data acquisition. We demonstrate imaging rates of 120 ms per cell at sub-μm resolution, that allow extraction of complex cellular phenotypes, exemplified by imaging of cell clusters, receptor distribution, and the analysis of endosomal size changes.