The quantum Hall effect arises from the cyclotron motion of charge carriers in two-dimensional systems. However, the ground states related to the integer and fractional quantum Hall effect, respectively, are of entirely different origin(1-5). The former can be explained within a single-particle picture; the latter arises from electron correlation effects governed by Coulomb interaction. The prerequisite for the observation of these effects is extremely smooth interfaces of the thin film layers to which the charge carriers are confined. So far, experimental observations of such quantum transport phenomena have been limited to a few material systems based on silicon, III-V compounds and graphene(1-9). In ionic materials, the correlation between electrons is expected to be more pronounced than in the conventional heterostructures, owing to a large effective mass of charge carriers. Here we report the observation of the fractional quantum Hall effect in MgZnO/ZnO heterostructures grown by molecular-beam epitaxy, in which the electron mobility exceeds 180,000 cm(2) V(-1) s(-1). Fractional states such as v = 4/3, 5/3 and 8/3 clearly emerge, and the appearance of the v = 2/5 state is indicated. The present study represents a technological advance in oxide electronics that provides opportunities to explore strongly correlated phenomena in quantum transport of dilute carriers.