The geometry of Hamiltonian’s eigenstates is encoded in the quantum geometric tensor (QGT), containing both the Berry curvature, central to the description of topological matter, and the quantum metric. So far, the full QGT has been measured only in Hermitian systems, where the role of the quantum metric is mostly limited to corrections. On the contrary, in non-Hermitian systems, and, in particular, near exceptional points, the quantum metric is expected to diverge and to often play a dominant role, for example, in the enhanced sensing and in wave packet dynamics. In this Letter, we report the first experimental measurement of the quantum metric in a non-Hermitian system. The specific platform under study is an organic microcavity with exciton-polariton eigenstates, which demonstrate exceptional points. We measure the quantum metric’s divergence, and we determine the scaling exponent n=−1.01±0.08, which is in agreement with the theoretical description of second-order exceptional points.