The white dwarf star G29-38 has an infrared excess which may be due to a cool low-mass companion, probably a brown dwarf, or to circumstellar dust. If the excess is due to dust, then changes in luminosity of the white dwarf, which is a ZZ Ceti variable, may cause the infrared excess to vary in phase with the optical pulsations. We have therefore obtained simultaneous optical and infrared light curves of G29-38 to search for variability of the excess. The known 614s period of G29-39 is seen at B and J, with amplitudes and phases which are in excellent agreement with the predictions of adiabatic, g-mode pulsation theory. No variability with a 614 s period is found at K above that expected from the white dwarf photosphere. We have discovered two significant periodicities in the K light curve at 181 ± 10 s and 243 ± 15 s. These periods are not found at shorter wavelengths, and we therefore conclude that they must be due to variations in the strength of the infrared excess, rather than the photospheric emission from the white dwarf. We propose a model which invokes a dust ring around the white dwarf to explain the infrared excess and variability in this system. A detection of G29-38 at 10 μm at a flux level about 3 times that expected from a brown dwarf favors the dust model.