The crucial aim for 5G narrowband Internet of Things (NB-IoT) is to support massive connectivity with wide coverage area, low power consumption, low hardware complexity, and low data rate. Direct conversion receiver (DCR) has a simple structure to fulfill NB-IoT requirements. However, a significant degradation has been observed on the performance of orthogonal frequency division multiplexing (OFDM) systems with the DCR due to in-phase and quadrature imbalance (IQI) at RF front-end. Estimation and mitigation of IQI in OFDM systems require an iterative receiver at the expense of high complexity and power consumption. In this paper, OFDM with index modulation (OFDM-IM) is proposed as a promising candidate in order to meet the demands of NB-IoT use cases. OFDM-IM-based systems carry data information not only by modulated subcarriers but also by indices of fractionally used subcarriers. A non-iterative and efficient receiver that exploits inactive subcarriers is introduced to mitigate the effect of IQI for NB-IoT with OFDM-IM. Cyclic redundancy check algorithm is used to investigate the accuracy of the receiver under IQI. Theoretical analysis and computer-based simulations show that the proposed non-iterative receiver for OFDM-IM in NB-IoT under IQI works very well in various scenarios. Moreover, our findings show that the OFDM-IM under IQI provides higher signal-to-interference ratio in comparison with classical OFDM.