By virtue of the combined merits of flow cytometry and fluorescence microscopy, imaging flow cytometry (IFC) has become an established tool for cell analysis in diverse biomedical fields such as cancer biology, microbiology, immunology, hematology, and stem cell biology. However, the performance and utility of IFC are severely limited by the fundamental trade-off between throughput, sensitivity, and spatial resolution. Here we present an optomechanical imaging method that overcomes the trade-off by virtually freezing the motion of flowing cells on the image sensor to effectively achieve 1000 times longer exposure time for microscopy-grade fluorescence image acquisition. Consequently, it enables high-throughput IFC of single cells at >10,000 cells s-1 without sacrificing sensitivity and spatial resolution. The availability of numerous information-rich fluorescence cell images allows high-dimensional statistical analysis and accurate classification with deep learning, as evidenced by our demonstration of unique applications in hematology and microbiology.