This paper presents a high-resolution automotive multi-input multi-output (MIMO) radar with sparse arrays using beamspace matrix completion. Sparse arrays, while offering a larger aperture than uniform arrays with an equivalent number of antenna elements, suffer from higher sidelobe levels due to missing elements (holes). To address this issue, an array interpolation technique employing low-rank matrix completion through a Hankel matrix formation has been proposed. However, the computational demands of this approach make it imprac-tical for low-cost automotive radar sensors. To overcome this challenge, we propose a subarray-based beamspace approach, reducing the dimensions of the Hankel matrix for efficient matrix completion in sparse arrays within automotive MIMO radar systems. Numerical simulations validate the effectiveness of our approach, focusing on a one-dimensional sparse linear array (SLA) and assessing various performance metrics.