The study of formation of heavy quarkonia in relativistic heavy-ion collisions provides important insight into the properties of the produced high-density QCD medium. Lattice QCD studies show sequential suppression of quarkonia states with increasing temperature; which affirms that a full spectroscopy can provide us a thermometer for the matter produced under extreme conditions in relativistic heavy-ion collisions and one of the most direct probes of deconfinement. Muons from the decay of charmonium resonances are detected in ALICE experiment in $p + p$ and Pb + Pb collisions with a muon spectrometer, covering the forward rapidity region $(2.5 < y < 4)$. The analysis of the inclusive $J/\psi$ production in the first Pb + Pb data collected in the fall of 2010 at a centre of mass energy of $\sqrt{^{s}NN} = 2.76$ TeV is discussed. Preliminary results on the nuclear modification factor $(R_{AA})$ and the central to peripheral nuclear modification factor $(R_{CP})$ are presented.