Moving Object Detection (MOD) is a crucial task for the Autonomous Driving pipeline. MOD is usually handled via 2-stream convolutional architectures that incorporates both appearance and motion cues, without considering the inter-relations between the spatial or motion features. In this paper, we tackle this problem through multi-head attention mechanisms, both across the spatial and motion streams. We propose MODETR; a Moving Object DEtection TRansformer network, comprised of multi-stream transformer encoders for both spatial and motion modalities, and an object transformer decoder that produces the moving objects bounding boxes using set predictions. The whole architecture is trained end-to-end using bi-partite loss. Several methods of incorporating motion cues with the Transformer model are explored, including two-stream RGB and Optical Flow (OF) methods, and multi-stream architectures that take advantage of sequence information. To incorporate the temporal information, we propose a new Temporal Positional Encoding (TPE) approach to extend the Spatial Positional Encoding(SPE) in DETR. We explore two architectural choices for that, balancing between speed and time. To evaluate the our network, we perform the MOD task on the KITTI MOD [6] data set. Results show significant 5% mAP of the Transformer network for MOD over the state-of-the art methods. Moreover, the proposed TPE encoding provides 10% mAP improvement over the SPE baseline.