We report on the first measurement of the average mass and mass-to-light ratio of galaxy groups by analysing the weak lensing signal induced by these systems. The groups, which have velocity dispersions of 50-400 km/s, have been selected from the Canadian Network for Observational Cosmology Field Galaxy Redshift Survey (CNOC2). This survey allows the identification of a large number of groups with redshifts ranging from z=0.12-0.55, ideal for a weak lensing analysis of their mass distribution. For our analysis we use a sample of 50 groups which are selected on the basis of a careful dynamical analysis of group candidates. We detect a signal at the 99% confidence limit. The best fit singular isothermal sphere model yields an Einstein radius of 0.72+-0.29". This corresponds to a velocity dispersion of 274^{+48}_{-59} km/s (using photometric redshift distributions for the source galaxies), which is in good agreement with the dynamical estimate. Under the assumption that the light traces the mass, we find an average mass-to-light ratio of 191+-83 h Msun/Lsun in the restframe B band. Unlike dynamical estimates, this result is insensitive to problems associated with determining group membership. After correction of the observed mass-to-light ratio for luminosity evolution to z=0, we find 254+-110 h Msun/Lsun, lower than what is found for rich clusters. We use the observed mass-to-light ratio to estimate the matter density of the universe, for which we find Omega_m=0.19+-0.10 (Omega_Lambda=0), in good agreement with other recent estimates. For a closed universe, we obtain Omega_m=0.13+-0.07. Comment: Accepted for ApJ Letters 4 pages, 2 figures, uses emulateapj5.sty