Multipath is a challenging problem for radar-based localization systems, especially in indoor scenarios. Multipath is caused by the bounces from static objects like walls and furniture in the room creating false alarms (``ghosts'') in target detections. Although solutions for the multipath effect have been proposed for a range of radar sensing problems, the specific case of multipath recognition and mitigation for a colocated multiple-input-multiple-output (MIMO) radar remains unsolved. For MIMO radar, the different direction-of-arrival (DoA) and direction-of-departure (DoD) angles inhibit the use of beamforming with a virtual array for localizing the first-order ghosts. Additionally, the prior knowledge of the multipath geometry model (room layout and boundary) is not always accessible. Classical ray tracing methods to resolve multipath are hence, not practical. In this work, we exploit a linear relationship between the target and multipath ghosts in the range-Doppler map to propose a Hough-transform-based multipath recognition solution. The algorithm does not require prior multipath geometry information and applies to the various indoor environments for an MIMO radar. Simulation and measurement results demonstrate the effectiveness of the proposed algorithm.