Machine-to-machine (M2M) communications play an important role for applications that involve connections between a massive number of heterogeneous devices in home and industrial networks. For M2M networks, realizing low latency and high reliability is of great importance. In this paper, we show the great potential of polar-coded orthogonal frequency-division multiplexing (OFDM) to fulfill those requirements. We show that polar codes with list decoding plus cyclic redundancy check (CRC) can outperform state-of-the-art low-density parity-check (LDPC) codes at short block lengths. In addition, we introduce an efficient interleaver and constellation shaping for polar-coded high-order modulations, where a coded sequence is carefully mapped across subcarriers and modulation bits to exploit nonuniform reliability for higher diversity gains. Through computer simulations, we demonstrate that a significant gain greater than 2 dB can be achieved by quadratic polynomial permutation (QPP) interleaver with optimized parameters in comparison to the conventional random interleaver for high-order 256-ary quadrature-amplitude modulation (QAM) OFDM transmission in frequency-selective wireless channels.