Muon beam monitoring is indispensable for indirectly monitoring accelerator-produced neutrino beams in real time. Though Si photodiodes and ionization chambers have been successfully used as muon monitors at the T2K experiment, sensors that are more radiation tolerant are desired for future operation. We have investigated the electron-multiplier tube (EMT) as a new sensor for muon monitoring. Secondary electrons produced by the passage of muons at dynodes are multiplied in the tube and produce signal. Two prototype detectors were installed at the T2K muon monitor location, and various EMT properties were studied based on in situ data taken with the T2K muon beam. The signal size is as expected based on calculation, and the EMTs show a sufficiently fast time response for bunch-by-bunch beam monitoring. The spill-by-spill intensity resolution is 0.4%, better than the required value (1%). Signal linearity within $pm$1% is achieved at proton beam powers up to 460 kW (with +250 kA focusing horn operation). A gradual signal decrease was observed during the initial exposure, due to the stabilization of dynode materials, before the response became stable within $pm$1%. This work demonstrates that EMTs are a good candidate for future muon monitoring at T2K, and may also have other more general applications.