Ghost imaging is a technique used to produce an object's image without using a spatially resolving detector. Here we develop a technique we term "ghost cytometry," an image-free ultrafast fluorescence "imaging" cytometry based on a single-pixel detector. Spatial information obtained from the motion of cells relative to a static randomly patterned optical structure is compressively converted into signals that arrive sequentially at a single-pixel detector. Combinatorial use of the temporal waveform with the intensity distribution of the random pattern allows us to computationally reconstruct cell morphology. More importantly, we show that applying machine-learning methods directly on the compressed waveforms without image reconstruction enables efficient image-free morphology-based cytometry. Despite a compact and inexpensive instrumentation, image-free ghost cytometry achieves accurate and high-throughput cell classification and selective sorting on the basis of cell morphology without a specific biomarker, both of which have been challenging to accomplish using conventional flow cytometers.