Reinforcement learning has achieved promising results on robotic control tasks but struggles to leverage information effectively from multiple sensory modalities that differ in many characteristics. Recent works construct auxiliary losses based on reconstruction or mutual information to extract joint representations from multiple sensory inputs to improve the sample efficiency and performance of reinforcement learning algorithms. However, the representations learned by these methods could capture information irrelevant to learning a policy and may degrade the performance. We argue that compressing information in the learned joint representations about raw multimodal observations is helpful, and propose a multimodal information bottleneck model to learn task-relevant joint representations from egocentric images and proprioception. Our model compresses and retains the predictive information in multimodal observations for learning a compressed joint representation, which fuses complementary information from visual and proprioceptive feedback and meanwhile filters out task-irrelevant information in raw multimodal observations. We propose to minimize the upper bound of our multimodal information bottleneck objective for computationally tractable optimization. Experimental evaluations on several challenging locomotion tasks with egocentric images and proprioception show that our method achieves better sample efficiency and zero-shot robustness to unseen white noise than leading baselines. We also empirically demonstrate that leveraging information from egocentric images and proprioception is more helpful for learning policies on locomotion tasks than solely using one single modality.