Epitaxial thin films of multiferroic perovskite BiMnO3 were synthesized on SrTiO3 substrates, and orbital ordering and magnetic properties of the thin films were investigated. The ordering of the Mn^{3+} e_g orbitals at a wave vector (1/4 1/4 1/4) was detected by Mn K-edge resonant x-ray scattering. This peculiar orbital order inherently contains magnetic frustration. While bulk BiMnO3 is known to exhibit simple ferromagnetism, the frustration enhanced by in-plane compressive strains in the films brings about cluster-glass-like properties.