Root Cause Analysis (RCA) is essential for pinpointing the root causes of failures in microservice systems. Traditional data-driven RCA methods are typically limited to offline applications due to high computational demands, and existing online RCA methods handle only single-modal data, overlooking complex interactions in multi-modal systems. In this paper, we introduce OCEAN, a novel online multi-modal causal structure learning method for root cause localization. OCEAN employs a dilated convolutional neural network to capture long-term temporal dependencies and graph neural networks to learn causal relationships among system entities and key performance indicators. We further design a multi-factor attention mechanism to analyze and reassess the relationships among different metrics and log indicators/attributes for enhanced online causal graph learning. Additionally, a contrastive mutual information maximization-based graph fusion module is developed to effectively model the relationships across various modalities. Extensive experiments on three real-world datasets demonstrate the effectiveness and efficiency of our proposed method.