The LHC heavy ion physics program aims at investigating the properties of strongly interacting matter at extreme energy density where the formation of the Quark Gluon Plasma is expected. Among the most promising observables, heavy quarkonium states are especially relevant since they provide, via their leptonic decays, an essential probe of the earliest and hottest stages of heavy ion collisions. ALICE (A Large Ion Collider Experiment) will be the only detector dedicated to the study of nucleus-nucleus collisions at the LHC. Heavy flavors will be measured in ALICE through the hadronic channel as well as with (di-)electrons and with (di-)muons. After a description of the ALICE muon spectrometer, its expected performances for (di-)muon measurements will be reviewed.