The interaction of an electromagnetic wave with a two-dimensional electron gas subjected to a magnetic field and a weak periodic potential is investigated. The electron - impurity interaction is included to the lowest order. The periodic modulation of the Landau states has a profound effect on the optical conductivity. Simultaneous excitation of an electron - hole pair contributes significantly to the absorption around and below the cyclotron frequency. This is in contrast to a uniform electron gas under a perpendicular magnetic field where electron - hole pair excitations are absent.