State-of-the-art optoacoustic tomographic imaging systems have been shown to attain three-dimensional (3D) frame rates of the order of 100 Hz. While such a high volumetric imaging speed is beyond reach for other bio-imaging modalities, it may still be insufficient to accurately monitor some faster events occurring on a millisecond scale. Increasing the 3D imaging rate is usually hampered by the limited throughput capacity of the data acquisition electronics and memory used to capture vast amounts of the generated optoacoustic (OA) data in real time. Herein, we developed a sparse signal acquisition scheme and a total-variation-based reconstruction approach in a combined space–time domain in order to achieve 3D OA imaging at kilohertz rates. By continuous monitoring of freely swimming zebrafish larvae in a 3D region, we demonstrate that the new approach enables significantly increasing the volumetric imaging rate by using a fraction of the tomographic projections without compromising the reconstructed image quality. The suggested method may benefit studies looking at ultrafast biological phenomena in 3D, such as large-scale neuronal activity, cardiac motion, or freely behaving organisms.