Hybrid ARQ (H-ARQ) schemes enable wireless reliability with high transmission efficiency, which is demanded for battery-operated low-complexity applications, such as Internet of Things. We propose two schemes to enable type-II H-ARQ based on systematic polar codes. We introduce code inversion for polar codes to recover the message from the redundant bits only. The first scheme we propose is an H-ARQ based on half-rate polar codes and code inversion. The second scheme develops a more general H-ARQ technique assuming an arbitrary code rate. We provide a theoretical framework for calculation of the frame error rate in polar codes with incomplete codeword elements. Simulations show that the proposed schemes can achieve a significant performance gain up to 4 dB in terms of throughput efficiency compared with the state-of-the-art H-ARQ scheme used in the high-quality-of-service mode of the IEEE 802.15.6-2012 standard for wireless body area networks.