We present a direct determination of the mass of the system components in the soft X-ray transient A0620 -00. Infrared photometry during 1990 allows us to determine the double-humped quiescent light curve, which we then fit with an ellipsoidal model. We obtain solutions in the mass-ratio-inclination plane which, when combined with the rotational broadening and the K velocity of the secondary star obtained by Marsh, Robinson & Wood, allows us to determine the masses of the system components. Using a Monte Carlo error propagation technique, we determine the most likely values for the mass of the compact object (M1), the mass and radius of the secondary star (M2, R2) and the orbital separation (α). We obtain M1 = 10.0 Msun, M2 =0.6 Msun, R2 =0.8 Rsun and α = 4.3 Rsun. We find that the observed infrared colour of the secondary star is consistent with that of a star that probably lies between the zero-age and terminal-age main sequences. Using this colour in conjunction with Bailey's relation and our estimates for the radius of the secondary star, we limit the distance to lie in the range 660-1450 pc, where the most probable value is 1050 pc.