Results are presented from a search for heavy, right-handed muon neutrinos, ${N}_{\ensuremath{\mu}}$, and right-handed ${W}_{R}$ bosons, which arise in the left-right symmetric extensions of the standard model. The analysis is based on a $5.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ sample of proton-proton collisions at a center-of-mass energy of 7 TeV, collected by the CMS detector at the Large Hadron Collider. No evidence is observed for an excess of events over the standard model expectation. For models with exact left-right symmetry, heavy right-handed neutrinos are excluded at 95% confidence level for a range of neutrino masses below the ${W}_{R}$ mass, dependent on the value of ${M}_{{W}_{R}}$. The excluded region in the two-dimensional (${M}_{{W}_{R}}$, ${M}_{{N}_{\ensuremath{\mu}}}$) mass plane extends to ${M}_{{W}_{R}}=2.5\text{ }\text{ }\mathrm{TeV}$.