A search for the rare decays $B_s^0 to pi^+pi^-mu^+mu^-$ and $B^0 to pi^+pi^-mu^+mu^-$ is performed in a data set corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5-1.3 GeV/$c^2$ and with muon pairs that do not originate from a resonance are considered. The first observation of the decay $B_s^0 to pi^+pi^-mu^+mu^-$ and the first evidence of the decay $B^0 to pi^+pi^-mu^+mu^-$ are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be $mathcal{B}(B_s^0 to pi^+pi^-mu^+mu^-)=(8.6pm 1.5,({rm stat}) pm 0.7,({rm syst})pm 0.7,({rm norm}))times 10^{-8}$ and $mathcal{B}(B^0 to pi^+pi^-mu^+mu^-)=(2.11pm 0.51,({rm stat}) pm 0.15,({rm syst})pm 0.16,({rm norm}) )times 10^{-8}$, where the third uncertainty is due to the branching fraction of the decay $B^0to J/psi(to mu^+mu^-)K^*(890)^0(to K^+pi^-)$, used as a normalisation.
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