We present upper limits on the production of heavy neutral leptons (HNLs) decaying to 𝜇⁢𝜋 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 ×10²⁰ protons on target from the Fermilab Booster Neutrino Beam, which produces mainly muon neutrinos with an average energy of ≈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 |𝑈_𝜇⁢4|² of the extended PMNS mixing matrix in the range |𝑈_𝜇⁢4|²<(6.6–0.9)×10⁻⁷ for Dirac HNLs and |𝑈_𝜇⁢4|²<(4.7–0.7)×10⁻⁷ for Majorana HNLs, assuming HNL masses between 260 and 385 MeV and |𝑈_𝑒⁢4|² =|𝑈_𝜏⁢4|² =0.