We have obtained an H-band infrared light curve of the low-mass X-ray binary transient Nova Muscae 1991. We model the light curve as being due to the tidal distortion of the secondary star in the gravitational field of a black hole, and thus deduce the binary inclination to be 54 deg, with 90 per cent confidence limits of +20 deg/-15 deg. Combining this with previously published spectroscopic data, we determine the mass of the black hole to be in the range 4-11Msolar (90 per cent confidence). Using Bailey's relation and our estimates of the radius of the secondary star, we obtain a 90 per cent lower limit to distance of 2.8kpc and a firm upper limit of 4.0kpc.