The Tokai-to-Kamioka (T2K) neutrino experiment measures neutrino oscillations by using an almost pure muon neutrino beam produced at the J-PARC accelerator facility. The T2K muon monitor was installed to measure the direction and stability of the muon beam which is produced in conjunction with the muon neutrino beam. The systematic error in the muon beam direction measurement was estimated, using data and MC simulation, to be 0.28 mrad. During beam operation, the proton beam has been controlled using measurements from the muon monitor and the direction of the neutrino beam has been tuned to within 0.3 mrad with respect to the designed beam-axis. In order to understand the muon beam properties, measurement of the absolute muon yield at the muon monitor was conducted with an emulsion detector. The number of muon tracks was measured to be $(4.06\pm 0.05\pm 0.10)\times 10^4$ cm $^{-2}$ normalized with $4\times 10^{11}$ protons on target with 250 kA horn operation. The result is in agreement with the prediction, which is corrected based on hadron production data.