  In this Letter we present calibrated observations of the average mass of
galaxies with 22< I < 25 in the Hubble Deep Field. We measure the mean mass
profile using the statistical gravitational lens distortion of faint blue
background galaxies, based on 2221 foreground-background pairs. The observed
weak lensing distortion is calibrated via full 3-D simulations and other HST
data on a foreground cluster of known mass. Inside a projected radius of 5
arcsec we find a 3\sigma detection of shear. Fitting to an isothermal mass
distribution, we find a shear of 0.066^{+0.018}_{-0.019} at a radius of
2\arcsec\ (\sim 8 ~ h^{-1} kpc). The (1\sigma) limits on the parameters for the
truncated isothermal model are \sigma_v =185^{+30}_{-35} km s^{-1}, r_{outer}
\ge 15 ~ h^{-1} kpc, and r_{core}= 0.6^{+1.3}_{-0.6} ~ h^{-1} kpc. This
corresponds to an average galaxy mass interior to 20 h^{-1} kpc of
5.9^{+2.5}_{-2.7}\times 10^{11} h^{-1} M_\odot. Inside 10 h^{-1} kpc, we find
an average rest-frame V band mass-to-light ratio of 11.4^{+6.0}_{-6.7} h
(M/L_V)_\odot.
