Orthogonal frequency division multiplexing with index modulation (OFDM-IM) is a promising technique for next-generation wireless communications due to its superior error performance and flexibility. However, as a type of multi-carrier modulation, it suffers from a high peak-to-average power ratio (PAPR), which can compromise transmission reliability. Therefore, in this paper, a polar-coded PAPR reduction scheme based on hybrid index modulation (PC-HIM) for OFDM-IM is proposed. Also, the proposed framework employs sets of various frozen bits and spatial modulation (SM) to solve the high PAPR issue in OFDM-IM systems. At the receiving side, the detection of the activated antennas status facilitate the recovery of selected frozen bit set, whose indices are embedded in the SM operations. Therefore, the need for transmitting side information, which is a necessary process in probabilistic PAPR reduction schemes, can be eliminated. Further, to enhance detection accuracy, a construction method for frozen bit sets based on Hadamard matrix is proposed. Additionally, to address the high complexity inherent in the proposed PC-HIM PAPR reduction framework, a low-complexity version, termed LC-PC-HIM, is proposed. This framework simplifies both the transmitting and receiving operations through a redesign of the information processing procedures and the selected frozen bit set detection step. Simulation results demonstrate that the proposed PAPR reduction scheme (PC-HIM and LC-PC-HIM) outperforms existing polar code-based PAPR reduction schemes by at most 12.5%, delivering the most effective PAPR reduction performance. Furthermore, the proposed receiving approach achieves error performance comparable to that of a receiver utilizing perfect side information.