A new heavy gauge boson, W', decaying to a muon and a neutrino, is searched for in pp collisions at a centre-of-mass of 7 TeV. The data, collected with the CMS detector at the LHC, correspond to an integrated luminosity of 36 inverse picobarns. No significant excess of events above the standard model expectation is found in the transverse mass distribution of the muon-neutrino system. Masses below 1.40 TeV are excluded at the 95% confidence level for a sequential standard-model-like W'. The W' mass lower limit increases to 1.58 TeV when the present analysis is combined with the CMS result for the electron channel.