Path planning among dynamic obstacles is a fundamental problem in Robotics with numerous applications. In this work, we investigate a problem called Multi-Objective Path Planning with Dynamic Obstacles (MOPPwDO), which requires finding collision-free Pareto-optimal paths amid obstacles moving along known trajectories while simultaneously optimizing multiple conflicting objectives, such as arrival time, communication robustness and obstacle clearance. Most of the existing multi-objective A*-like planners consider no dynamic obstacles, and naively applying them to address MOPPwDO can lead to large computation times. On the other hand, efficient algorithms such as Safe-Interval Path Planing (SIPP) can handle dynamic obstacles but for a single objective. In this work, we develop an algorithm called MO-SIPP by leveraging both the notion of safe intervals from SIPP to efficiently represent the search space in the presence of dynamic obstacles, and search techniques from multi-objective A* algorithms. We show that MO-SIPP is guaranteed to find the entire Pareto-optimal front, and verify MO-SIPP with extensive numerical tests with two and three objectives. The results show that the MO-SIPP runs up to an order of magnitude faster than the conventional alternates.