E-commerce order fulfillment is increasingly disrupted by natural events such as pandemics, hurricanes, and floods. This study investigates order assignment decisions considering warehouse disruption risk, order-class priority, and shipping costs. We develop a stochastic dynamic programming model for the order assignment problem. Our analysis reveals a switching-curve policy for order assignment. We find that disruption risk significantly affects the order assignment decision, with optimal switching thresholds decreasing as the disruption rate increases. To efficiently compute these thresholds, we develop three index-based heuristic policies. Among them, our improvement heuristic achieves an average optimality gap of 7.21%, outperforming the myopic policy (8.48%) and the least shipping cost heuristic (14.17%). Through a comprehensive numerical study, we uncover several important insights. Disruption and recovery rates have nonlinear effects on order fulfillment costs. Specifically, while investing in mechanisms to enhance recovery speed is beneficial, the gains become progressively smaller as recovery becomes faster. Additionally, shared order-processing capacity at warehouses with class-wise priority can prove a more effective strategy than maintaining dedicated capacities for each order class. This research provides actionable strategies for managing e-commerce fulfillment under warehouse disruption risks, enhancing operational efficiency and cost management.