The rapid rotation of Be stars may be caused in some cases by past mass and angular momentum accretion in an interacting binary in which the mass donor is currently viewed as a small, hot subdwarf stripped of its outer envelope. Here we report on the spectroscopic detection of such a subdwarf in the Be binary system FY Canis Majoris from the analysis of data acquired by the IUE spacecraft and KPNO Coude Feed Telescope over the course of 16 and 21yr, respectively. We present a double-lined spectroscopic orbit for the binary based on radial velocities from the IUE spectra and use the orbital solutions with a Doppler tomography algorithm to reconstruct the components' UV spectra. The subdwarf is hot (T_eff_=45+/-5kK) and has a mass of about 1.3M_{sun} and a radius of about 0.6R{sun}_. It contributes about 4% as much flux as the Be star does in the FUV. We also present observations of the H{alpha} and HeI{lambda}6678 emission features that are formed in the circumstellar disk of the Be star.