The suppressed decay $\Lambda^{0}_{b}\rightarrow p\pi^{-}\mu^{+}\mu^{-}$,
excluding the $J/\psi$ and $\psi(2S)\rightarrow \mu^{+}\mu^{-}$ 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 $\Lambda^{0}_{b}\rightarrow p\pi^{-}\mu^{+}\mu^{-}$ branching
fraction is measured relative to the $\Lambda^{0}_{b}\rightarrow
J/\psi(\rightarrow \mu^{+}\mu^{-})p\pi^{-}$ branching fraction giving
\begin{align} \nonumber
\frac{\mathcal{B}(\Lambda^{0}_{b}\rightarrow
p\pi^{-}\mu^{+}\mu^{-})}{\mathcal{B}({\Lambda^{0}_{b}\rightarrow
J/\psi(\rightarrow \mu^{+}\mu^{-})p\pi^{-}})} &= 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.