Accurate flow predictions are critical for energy-optimal path planning of AUVs with endurance requirements. However, the complex dynamics of ocean currents make it difficult to achieve accurate flow predictions. For an AUV with flow and location sensing capabilities, one can optimize vehicle actions so that the flow information collected along the vehicle path reduces flow prediction uncertainty, referred to as active flow perception. In this paper, we propose an energy-optimal path planning approach that incorporates active flow perception. The proposed approach achieves the objectives of vehicle energy consumption minimization and flow prediction uncertainty reduction. To quantify flow prediction uncertainty, an empirical flow model parameterized using the proper orthogonal decomposition (POD) is constructed based on historical data. Assuming negligible unmodeled dynamics in the POD model, the flow prediction uncertainty is evaluated by the Cramer-Rao (CR) bound of estimated model parameters. To establish active flow perception combined with energy optimal path planning, we formulate the cost to be minimized during path planning in terms of vehicle energy using estimated flow parameters and CR bound. Through simulations, the proposed approach is compared with approaches that plan energy-optimal paths using i) true flow and ii) flow predictions without active flow perception. Simulation results demonstrate the satisfactory energy-saving performance of the proposed approach.