We report HST/Faint Object Spectrograph (FOS) and Faint Object Camera (FOC) observations of X-ray Nova Muscae 1991 obtained on 1991 May 14-15. The FOS spectrum covering 1581-4807 angstrom shows a clear 2200 angstrom absorption feature. With a fit to the continuum considering the interstellar extinction and a power-law spectrum (f(nu) is-proportional-to nu(alpha)), we determine a color excess E(B - V) approximately 0.29 and a power-law slope of alpha approximately 0.30, which approximates a canonical accretion disk spectrum. By fitting a simple model of a steady state blackbody accretion disk around a black hole to the FOS spectrum and multiepoch data in the optical, UV, and X-ray bands, we estimate the lower limit mass of the central compact object M(min), the radius of the accretion disk R(out), the maximum orbital period P(max), and the upper limit mass transfer rate M(max) during the decline for several assumed values of the disk inclination angle i and distance D to the source. We find that M decays exponentially with a characteristic time of approximately 43 days. The cooling front predicted by the disk instability models to occur in the outer disk when T < 10(4) K should have been observable, but was not seen.