Autonomous vehicles (AVs) must share the driving space with other drivers and often employ conservative motion planning strategies to ensure safety. These conservative strategies can negatively impact AV's performance and significantly slow traffic throughput. Therefore, to avoid conservatism, we design an interaction-aware motion planner for the ego vehicle (AV) that interacts with surrounding vehicles to perform complex maneuvers in a locally optimal manner. Our planner uses a neural network-based interactive trajectory predictor and analytically integrates it with model predictive control (MPC). We solve the MPC optimization using the alternating direction method of multipliers (ADMM) and prove the algorithm's convergence. We provide an empirical study and compare our method with a baseline heuristic method.