Production cross sections of muons from semi-leptonic decays of charm and beauty hadrons were measured at forward rapidity (2.5 < y < 4) in proton-proton (pp) collisions at a centre-of-mass energy s = 5.02 TeV with the ALICE detector at the CERN LHC. The results were obtained in an extended transverse momentum interval, 2 < p_T< 20 GeV/c, and with an improved precision compared to previous measurements performed in the same rapidity interval at centre-of-mass energies s = 2.76 and 7 TeV. The p_T- and y-differential production cross sections as well as the p_T-differential production cross section ratios between different centre-of-mass energies and different rapidity intervals are described, within experimental and theoretical uncertainties, by predictions based on perturbative QCD. [Figure not available: see fulltext.]