The Maunakea Spectroscopic Explorer (MSE) is a next-generation observatory, designed to provide highly multiplexed, multi-object spectroscopy over a wide field of view. The observatory will consist of (1) a telescope with an 11.25 m aperture, (2) a 1.5 square-degree science field of view, (3) fibre optic positioning and transmission systems, and (4) a suite of low (R=3000), moderate (R=6000) and high resolution (R=40,000) spectrographs. The Fibre Transmission System (FiTS) consists of 4332 optical fibres, designed to transmit the light from the telescope prime focus to the dedicated spectrographs. The ambitious science goals of MSE require the Fibre Transmission System to deliver performance well beyond the current state of the art for multi-fibre systems, e.g., the sensitivity to observe magnitude 24 objects over a very broad wavelength range (0.37 - 1.8 microns) while achieving relative spectrophotometric accuracy of <3% and radial velocity precision of 20 km/s.