A novel type of magnetoresistance oscillations is observed in high-mobility AlGaAs/GaAs heterojunctions with a holographically induced lateral periodic modulation in one direction. Theoretically, the effect is shown to result from an oscillatory dependence of the bandwidth of the modulation-broadened Landau levels of the two-dimensional electron system on the band index, which leads in high-mobility samples to a strongly anisotropic oscillating contribution to the conductivity tensor. The oscillations, periodic in B-1, reflect the commensurability of cyclotron diameter at the Fermi energy and modulation period.