We report striking changes in the broadband spectrum of the compact jet of the black hole transient MAXI J1836–194 over state transitions during its discovery outburst in 2011. A fading of the optical-infrared (IR) flux occurred as the source entered the hard-intermediate state, followed by a brightening as it returned to the hard state. The optical-IR spectrum was consistent with a power law from optically thin synchrotron emission, except when the X-ray spectrum was softest. By fitting the radio to optical spectra with a broken power law, we constrain the frequency and flux of the optically thick/thin break in the jet synchrotron spectrum. The break gradually shifted to higher frequencies as the source hardened at X-ray energies, from ~1011 to ~4 × 1013 Hz. The radiative jet luminosity integrated over the spectrum appeared to be greatest when the source entered the hard state during the outburst decay (although this is dependent on the high-energy cooling break, which is not seen directly), even though the radio flux was fading at the time. The physical process responsible for suppressing and reactivating the jet (neither of which are instantaneous but occur on timescales of weeks) is uncertain, but could arise from the varying inner accretion disk radius regulating the fraction of accreting matter that is channeled into the jet. This provides an unprecedented insight into the connection between inflow and outflow, and has implications for the conditions required for jets to be produced, and hence their launching process. Based on observations collected at the European Southern Observatory, Chile, under ESO Program IDs 087.D-0914 and 089.D-0970.