Muonium has been studied in muon-irradiated water over a wide range of conditions, from standard temperature and pressure (STP) up to 350 bar and up to 420°C, corresponding to water densities from 1.0 down to 0.1 g cm^-3. This is the first report of muonium in supercritical water. Muonium was unambiguously identified from its spin precession frequencies in small transverse magnetic fields. The hyperfine constant was determined and found to be similar to the published values for muonium in water at STP and in vacuum. Muonium was found to be long-lived over the whole range of conditions studied. The fraction of muons which form muonium was found to vary markedly over the density range studied. Correlation of the muonium fraction with the ionic product of water suggests a common cause, such as the rate of proton transfer between molecules involved in the radiolysis of water and the formation of MuOH, which competes with muonium formation.