A search for the nonresonant Λ_c⁺ → pμ⁺μ^- decay is performed using proton-proton collision data recorded at a center-of-mass energy of 13 TeV by the LHCb experiment, corresponding to an integrated luminosity of 5.4 fb^-1. No evidence for the decay is found in the dimuon invariant-mass regions where the expected contributions of resonances is subdominant. The upper limit on the branching fraction of the Λ_c⁺ → pμ⁺μ^- decay is determined to be 2.9(3.2) x 10^-8 at 90%(95%) confidence level. The branching fractions in the dimuon invariant-mass regions dominated by the η, ρ and ω resonances are also determined.