A search for the rare η→μ^{+}μ^{-}μ^{+}μ^{-} double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers during 2017 and 2018 and corresponding to an integrated luminosity of 101 fb^{-1}. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the η→μ^{+}μ^{-} decay as normalization, the branching fraction B(η→μ^{+}μ^{-}μ^{+}μ^{-})=[5.0±0.8(stat)±0.7(syst)±0.7(B_{2μ})]×10^{-9} is measured, where the last term is the uncertainty in the normalization channel branching fraction. This work achieves an improved precision of over 5 orders of magnitude compared to previous results, leading to the first measurement of this branching fraction, which is found to agree with theoretical predictions.