Efficient exploration in deep cooperative multi-agent reinforcement learning (MARL) still remains challenging in complex coordination problems. In this paper, we introduce a novel Episodic Multi-agent reinforcement learning with Curiosity-driven exploration, called EMC. We leverage an insight of popular factorized MARL algorithms that the ``induced" individual Q-values, i.e., the individual utility functions used for local execution, are the embeddings of local action-observation histories, and can capture the interaction between agents due to reward backpropagation during centralized training. Therefore, we use prediction errors of individual Q-values as intrinsic rewards for coordinated exploration and utilize episodic memory to exploit explored informative experience to boost policy training. As the dynamics of an agent's individual Q-value function captures the novelty of states and the influence from other agents, our intrinsic reward can induce coordinated exploration to new or promising states. We illustrate the advantages of our method by didactic examples, and demonstrate its significant outperformance over state-of-the-art MARL baselines on challenging tasks in the StarCraft II micromanagement benchmark.