We report the first direct observation of the oxygen-isotope ((16)O/(18)O) effect on the in-plane penetration depth lambda(ab) in a nearly optimally doped YBa(2)Cu(3)O(7-delta) film using the novel low-energy muon-spin rotation technique. Spin-polarized low-energy muons are implanted in the film at a known depth z beneath the surface and process in the local magnetic field B(z). This feature allows us to measure directly the profile B(z) of the magnetic field inside the superconducting film in the Meissner state and to make a straightforward determination of lambda(ab). A substantial isotope shift Delta lambda(ab)/lambda(ab)=2.8(1.0)% at 4 K is observed, implying that the in-plane effective supercarrier mass m*(ab) is oxygen-isotope dependent with Delta m*(ab)/m*(ab)=5.5(2.0)%. These results are in good agreement with magnetization measurements on powder samples.