We search for excited and exotic muon states mu* using an integrated luminosity of 371 pb(-1) of p[over]p collision data at sqrt[s]=1.96 TeV. We search for associated production of mumu* followed by the decay mu*-->mugamma. We compare the data to model predictions as a function of the mass of the excited muon M(mu*), the compositeness energy scale Lambda, and the gauge coupling factor f. No signal above the standard model expectation is observed. We exclude 107<M(mu*)<853 GeV/c(2) for Lambda=M(mu*) in the contact interaction model, and 100<M(mu*)<410 GeV/c(2) for f/Lambda=10(-2) GeV-1 in the gauge-mediated model, both at the 95% confidence level.