In this paper, we study the dynamic meal delivery routing problem (MDRP) with time-sensitive customers. The multi-objective MDRP optimization model is developed to maximize customer satisfaction and minimize delay penalty cost and riding cost. To solve the dynamic MDRP, a novel waiting strategy is proposed to divide the dynamic problem into a series of static subproblems. This waiting strategy utilizes the decision threshold to determine rerouting points based on the number of dynamic meal orders. Meanwhile, time-sensitive priority is introduced to accelerate assignment and routing decisions for orders from customers with high time sensitivity. For each static subproblem, a hybrid AGA–ALNS algorithm that incorporates the adaptive genetic algorithm and adaptive large neighborhood search is developed to improve both the global and local search capabilities of the genetic algorithm. We validate the performance of the proposed waiting strategy and the AGA–ALNS algorithm through numerical instances. In addition, managerial insights are obtained from sensitivity analysis experiments.