In this work, we present an approach to deep visuomotor control using structured deep dynamics models. Our deep dynamics model, a variant of SE3-Nets, learns a low-dimensional pose embedding for visuomotor control via an encoder-decoder structure. Unlike prior work, our dynamics model is structured: given an input scene, our network explicitly learns to segment salient parts and predict their pose-embedding along with their motion modeled as a change in the pose space due to the applied actions. We train our model using a pair of point clouds separated by an action and show that given supervision only in the form of point-wise data associations between the frames our network is able to learn a meaningful segmentation of the scene along with consistent poses. We further show that our model can be used for closed-loop control directly in the learned low-dimensional pose space, where the actions are computed by minimizing error in the pose space using gradient-based methods, similar to traditional model-based control. We present results on controlling a Baxter robot from raw depth data in simulation and in the real world and compare against two baseline deep networks. Our method runs in real-time, achieves good prediction of scene dynamics and outperforms the baseline methods on multiple control runs. Video results can be found at: https://rse-lab.cs.washington.edu/se3-structured-deep-ctrl/