The international Muon Ionization Cooling Experiment (MICE) will perform a systematic investigation of ionization cooling with muon beams of momentum between 140 and 240\,MeV/c at the Rutherford Appleton Laboratory ISIS facility. The measurement of ionization cooling in MICE relies on the selection of a pure sample of muons that traverse the experiment. To make this selection, the MICE Muon Beam is designed to deliver a beam of muons with less than ∼1\% contamination. To make the final muon selection, MICE employs a particle-identification (PID) system upstream and downstream of the cooling cell. The PID system includes time-of-flight hodoscopes, threshold-Cherenkov counters and calorimetry. The upper limit for the pion contamination measured in this paper is fπ<1.4% at 90\% C.L., including systematic uncertainties. Therefore, the MICE Muon Beam is able to meet the stringent pion-contamination requirements of the study of ionization cooling.Department of Energy and National Science Foundation (U.S.A.), the Instituto Nazionale di Fisica Nucleare (Italy), the Science and Technology Facilities Council (U.K.), the European Community under the European Commission Framework Programme 7 (AIDA project, grant agreement no. 262025, TIARA project, grant agreement no. 261905, and EuCARD), the Japan Society for the Promotion of Science and the Swiss National Science Foundation, in the framework of the SCOPES programme