We developed a silicon (Si) dielectric diplexer module for 600-GHz-band frequency-division multiplexing wireless communication. This diplexer was developed based on Si dielectric waveguide technology, which provides low-loss transmission characteristics compared with the conventional metallic terahertz-transmission platform, such as metallic hollow waveguides. It includes straight waveguides based on an effective medium composed of Si and air, and a coupler comprising of two adjacent unclad Si waveguides. Furthermore, for the communication system integration, we developed a practical and low-insertion loss module with WR1.5 metallic hollow waveguide input-output interfaces and modularized the diplexer. We performed transmission measurement experiments with the fabricated diplexer module and achieved 3-dB bandwidths of 101 and 37 GHz, and crosstalk of -34 dB at 680 GHz and -41 dB at 618 GHz in the cross and bar directions, respectively. Finally, we performed a two-channel wireless communication experiment using the developed diplexer module in the 600-GHz band. We achieved error-free communication at 10 and 6 Gbit/s on the cross and bar channels, respectively. In addition, we achieved a data rate of up to 12.5 Gbit/s at the forward error correction limits for both channels.