We present the first measurement of the cross section of Cabibbo-suppressed Λ baryon production, using data collected with the MicroBooNE detector when exposed to the neutrinos from the main injector beam at the Fermi National Accelerator Laboratory. The data analyzed correspond to 2.2×10^{20} protons on target running in neutrino mode, and 4.9×10^{20} protons on target running in anti-neutrino mode. An automated selection is combined with hand scanning, with the former identifying five candidate Λ production events when the signal was unblinded, consistent with the GENIE prediction of 5.3±1.1 events. Several scanners were employed, selecting between three and five events, compared with a prediction from a blinded Monte Carlo simulation study of 3.7±1.0 events. Restricting the phase space to only include Λ baryons that decay above MicroBooNE's detection thresholds, we obtain a flux averaged cross section of 2.0_{-1.7}^{+2.2}×10^{-40} cm^{2}/Ar, where statistical and systematic uncertainties are combined.