The properties of the high-density medium formed in heavy-ion collisions at LHC can be investigated through heavy-quark production. These quarks are created in the initial hard collision processes with short formation time and are expected to lose energy while passing through the high-density strongly-interacting system. A complete understanding of heavy flavour production mechanisms in heavy-ion collisions requires the study of their production in proton-proton collisions. We will describe the ALICE muon spectrometer and then present the results on the production of single muons from heavy flavour decays at forward pseudo-rapidity (2.5 < eta < 4) in proton-proton collisions at s^1/2 = 7 TeV and Pb-Pb collisions at s^1/2_NN = 2.76 TeV. In particular, we will show the pt-differential production cross-section in proton-proton collisions and compare this to the perturbative QCD predictions as well as the nuclear modification factors R_AA and R_CP in Pb-Pb collisions.