A search for the baryon- and lepton-number violating decays ${B}^{0}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}}$ is performed at the LHCb experiment using data collected in proton-proton collisions at $\sqrt{s}=7$, 8 and 13 TeV, corresponding to integrated luminosities of 1, 2, and $6\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, respectively. No significant signal for ${B}^{0}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}}$ decays is found and the upper limits on the branching fractions are determined to be $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}})<2.6(3.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and $\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}})<12.1(14.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$, respectively, at 90% (95%) confidence level. These are the first limits on these decays to date.