A search for the baryon- and lepton-number violating decays B0→pμ- and Bs0→pμ- is performed at the LHCb experiment using data collected in proton-proton collisions at s=7, 8 and 13 TeV, corresponding to integrated luminosities of 1, 2, and 6  fb-1, respectively. No significant signal for B0→pμ- and Bs0→pμ- decays is found and the upper limits on the branching fractions are determined to be B(B0→pμ-)<2.6(3.1)×10-9 and B(Bs0→pμ-)<12.1(14.0)×10-9, respectively, at 90% (95%) confidence level. These are the first limits on these decays to date.