The suppressed decay $Λ^{0}_{b}\rightarrow pπ^{-}μ^{+}μ^{-}$, excluding the $J/ψ$ and $ψ(2S)\rightarrow μ^{+}μ^{-}$ resonances, is observed for the first time with a significance of 5.5 standard deviations. The analysis is performed with proton-proton collision data corresponding to an integrated luminosity of $3\mathrm{fb}^{-1}$ collected with the LHCb experiment. The $Λ^{0}_{b}\rightarrow pπ^{-}μ^{+}μ^{-}$ branching fraction is measured relative to the $Λ^{0}_{b}\rightarrow J/ψ(\rightarrow μ^{+}μ^{-})pπ^{-}$ branching fraction giving \begin{align} \nonumber \frac{\mathcal{B}(Λ^{0}_{b}\rightarrow pπ^{-}μ^{+}μ^{-})}{\mathcal{B}({Λ^{0}_{b}\rightarrow J/ψ(\rightarrow μ^{+}μ^{-})pπ^{-}})} &= 0.044\pm0.012\pm0.007, \end{align} where the first uncertainty is statistical and the second is systematic. This is the first observation of a $b\rightarrow d$ transition in a baryonic decay.