The Neutrinos at the Main Injector (NuMI) facility is a conventional neutrino beam which produces muon neutrinos by focusing a beam of mesons into a long evacuated decay volume. We have built four arrays of ionization chambers to monitor the position and intensity of the hadron and muon beams associated with neutrino production at locations downstream of the decay volume. This article describes the chambers construction, calibration, and commissioning in the beam.