A search for heavy Majorana neutrinos produced in the B − → π + μ − μ − decay mode is performed using 3     fb − 1 of integrated luminosity collected with the LHCb detector in p p collisions at center-of-mass energies of 7 and 8 TeV at the LHC. Neutrinos with masses in the range 250 to 5000 MeV and lifetimes from zero to 1000 ps are probed. In the absence of a signal, upper limits are set on the branching fraction B ( B − → π + μ − μ − ) as functions of neutrino mass and lifetime. These limits are on the order of 10 − 9 for short neutrino lifetimes of 1 ps or less. Limits are also set on the coupling between the muon and a possible fourth-generation neutrino.