We report on the first measurement of flux-integrated single differential cross sections for charged- current (CC) muon neutrino (νμ) scattering on argon with a muon and a proton in the final state, 40Ar (νμ,μp)X. The measurement was carried out using the Booster Neutrino Beam at the Fermi National Accelerator Laboratory and the MicroBooNE liquid argon time projection chamber de- tector with an exposure of 4.59 × 1019 protons on target. Events are selected to enhance the contribution of CC quasielastic (CCQE) interactions, reaching 81.1% of the final event sample. The data are reported in terms of a total cross section as well as single differential cross sections in final state muon and proton kinematics. We measure the integrated CCQE–like cross section of (4.93 ± 0.76stat ± 1.29sys) × 10−38cm2, in good agreement with theoretical calculations. The single differential cross sections are also in overall good agreement with theoretical predictions, except at very forward muon scattering angles that correspond to low momentum-transfer events.