We present upper limits on the production of heavy neutral leptons (HNLs) decaying to mu p pairs using data collected with the MicroBooNE liquid-argon time projection chamber (TPC) operating at Fermilab. This search is the first of its kind performed in a liquid-argon TPC. We use data collected in 2017 and 2018 corresponding to an exposure of 2.0 x 10(20) protons on target from the Fermilab Booster Neutrino Beam, which produces mainly muon neutrinos with an average energy of approximate to 800 MeV. HNLs with higher mass are expected to have a longer time of flight to the liquid-argon TPC than Standard Model neutrinos. The data are therefore recorded with a dedicated trigger configured to detect HNL decays that occur after the neutrino spill reaches the detector. We set upper limits at the 90% confidence level on the element vertical bar U-mu 4 vertical bar(2) of the extended PMNS mixing matrix in the range vertical bar U-mu 4 vertical bar(2) <(6.6-0.9) x 10(-7) for Dirac HNLs and vertical bar U-mu 4 vertical bar(2) <(4.7-0.7) x 10(-7) for Majorana HNLs, assuming HNL masses between 260 and 385 MeV and vertical bar U-e4 vertical bar(2) = vertical bar U-tau 4 vertical bar(2) = 0.