Gravitational microlensing offers a means of determining directly the masses of objects ranging from planets to stars, provided that the distances and motions of the lenses and sources can be determined. A globular cluster observed against the dense stellar field of the Galactic bulge presents ideal conditions for such observations because the probability of lensing is high and the distances and kinematics of the lenses and sources are well constrained. The abundance of low-mass objects in a globular cluster is of particular interest, because it may be representative of the very early stages of star formation in the Universe, and therefore indicative of the amount of dark baryonic matter in such clusters. Here we report a microlensing event associated with the globular cluster M22. We determine the mass of the lens to be 0.13(+0.03)(-0.02) solar masses. We have also detected six events that are unresolved in time. If these are also microlensing events, they imply that a non-negligible fraction of the cluster mass resides in the form of free-floating planetary-mass objects.