We demonstrate the first megahertz (MHz) repetition-rate, broadband terahertz (THz) source based on optical rectification in the organic crystal HMQ-TMS driven by a femtosecond Yb:fibre laser. Pumping at 1035 nm with 30 fs pulses, we achieve few-cycle THz emission with a smooth multi-octave spectrum that extends up to 6 THz at -30 dB, with conversion efficiencies reaching 10 4 and an average output power of up to 0.38 mW. We assess the thermal damage limit of the crystal and conclude a maximum fluence of similar to 1.8 mJ.cm(-2) at 10 MHz with a 1/e(2) pump beam diameter of 0.10 mm. We compare the performance of HMQ-TMS with the prototypical inorganic crystal gallium phosphide (GaP), yielding a tenfold electric field increase with a peak on-axis field strength of 7 kV.cm(-1) and almost double the THz bandwidth. Our results further demonstrate the suitability of organic crystals in combination with fibre lasers for repetition-rate scaling of broadband, high-power THz sources for time-domain spectroscopic applications.