We present the first clear evidence for a nuclear dependence of the transverse momentum distribution of massive muon pairs produced in hadronic interactions. Comparing the cross sections for high-mass dimuon production by incident negative pions (140 and 286 GeV) off tungsten and deuterium, we find that their ratio increases with the dimuon transverse momentum. The resulting difference in the mean transverse momentum squared amounts to 0.15±0.03 (syst.) GeV2/c2 and is shown to be independent of the dimuon mass and longitudinal momentum.