We investigate the variability of optical and near-infrared light curves of the X-ray binary GX 339-4 on a time-scale of days. We use the data in four filters from six intervals corresponding to the soft state and from four intervals corresponding to the quiescent state. In the soft state, we find prominent oscillations with an average period P = 1.772 +/- 0.003 d, which is offset from the measured orbital period of the system by 0.7 per cent. We suggest that the measured periodicity originates from the superhumps. In line with this interpretation, we find no periodicity in the quiescent state. The obtained period excess epsilon is below typical values found for cataclysmic variables for the same mass ratio of the binary. We discuss the implications of this finding in the context of superhump theory.