Considerable research efforts have been devoted to the development of motion planning algorithms, which form a cornerstone of the autonomous driving system (ADS). Nonetheless, acquiring an interactive and secure trajectory for the ADS remains challenging due to the complex nature of interaction modeling in planning. Modern planning methods still employ a uniform treatment of prediction outcomes and solely rely on collision-avoidance strategies, leading to suboptimal planning performance. To address this limitation, this paper presents a novel prediction-based interactive planning framework for autonomous driving. Our method incorporates interaction reasoning into spatio-temporal (s-t) planning by defining interaction conditions and constraints. Specifically, it records and continually updates interaction relations for each planned state throughout the forward search. We assess the performance of our approach alongside state-of-the-art methods in the CommonRoad environment. Our experiments include a total of 232 scenarios, with variations in the accuracy of prediction outcomes, modality, and degrees of planner aggressiveness. The experimental findings demonstrate the effectiveness and robustness of our method. It leads to a reduction of collision times by approximately 17.6% in 3-modal scenarios, along with improvements of nearly 7.6% in distance completeness and 31.7% in the fail rate in single-modal scenarios. For the community's reference, our code is accessible at https://github.com/ChenYingbing/IR-STP-Planner.