Understanding the mechanisms of cardiac disorders largely depends on availability of multi-dimensional and multiparametric imaging methods capable of quantitative assessment of cardiac morphology and function. The imaging modalities commonly employed in cardiac research, such as ultrasonography and magnetic resonance imaging, are lacking sufficient contrast and/or spatio-temporal resolution in 3D in order to reveal the multi-scale nature of rapid electromechanical activity in a beating heart. Our recently developed volumetric optoacoustic tomography (VOT) platform offers versatile observations of the heart function with rich optical contrast at otherwise unattainable temporal and spatial resolutions. Herein, we further advance the imaging performance by developing compressed acquisition scheme to boost the temporal resolution of VOT into the kilohertz range, thus enabling 3D mapping of electromechanical wave propagation in the heart. Experiments in isolated mouse hearts were performed by exciting the entire imaged tissue volume with nanosecond-duration laser pulses at 1 kHz repetition rate pulse operating at 532 nm and sparse tomographic signal sampling using a custom-made 512-element spherical matrix ultrasound array. By analyzing the strain maps obtained from the rapid VOT image sequence, it was possible to quantify the phase velocity of the electromechanical cardiac waves, in good agreement with previously reported values.