We present the first search for heavy neutral leptons (HNLs) decaying into νe^{+}e^{-} or νπ^{0} final states in a liquid-argon time projection chamber using data collected with the MicroBooNE detector. The data were recorded synchronously with the NuMI neutrino beam from Fermilab's main injector corresponding to a total exposure of 7.01×10^{20} protons on target. We set upper limits at the 90% confidence level on the mixing parameter |U_{μ4}|^{2} in the mass ranges 10≤m_{HNL}≤150 MeV for the νe^{+}e^{-} channel and 150≤m_{HNL}≤245 MeV for the νπ^{0} channel, assuming |U_{e4}|^{2}=|U_{τ4}|^{2}=0. These limits represent the most stringent constraints in the mass range 35<m_{HNL}<175 MeV and the first constraints from a direct search for νπ^{0} decays.