Purpose To achieve high temporal frame rate, high spatial resolution and full‐vocal‐tract coverage for three‐dimensional dynamic speech MRI by using low‐rank modeling and sparse sampling. Methods Three‐dimensional dynamic speech MRI is enabled by integrating a novel data acquisition strategy and an image reconstruction method with the partial separability model: (a) a self‐navigated sparse sampling strategy that accelerates data acquisition by collecting high‐nominal‐frame‐rate cone navigator sand imaging data within a single repetition time, and (b) are construction method that recovers high‐quality speech dynamics from sparse (k,t)‐space data by enforcing joint low‐rank and spatiotemporal total variation constraints. Results The proposed method has been evaluated through in vivo experiments. A nominal temporal frame rate of 166 frames per second (defined based on a repetition time of 5.99 ms) was achieved for an imaging volume covering the entire vocal tract with a spatial resolution of 2.2 × 2.2 × 5.0 mm3. Practical utility of the proposed method was demonstrated via both validation experiments and a phonetics investigation. Conclusion Three‐dimensional dynamic speech imaging is possible with full‐vocal‐tract coverage, high spatial resolution and high nominal frame rate to provide dynamic speech data useful for phonetic studies. Magn Reson Med 77:1619–1629, 2017. © 2016 International Society for Magnetic Resonance in Medicine