Context. S106, one of the best known bipolar HII regions, has been thoroughly studied and modeled at infrared, submillimeter, and millimeter wavelengths. This region is one of the nearest examples of the late stages of massive star formation, in which the newly formed star that ionizes it is still surrounded by vast amounts of gas and dust. However, little is known about the heavily obscured central source of this region, S106IR. Aims. We investigate the possible binarity of the central source is investigated; this binarity is considered to be likely given the high binarity fraction among massive stars. Methods. We have carried out visible and near-infrared photometric monitoring looking for short-term variability, and we took special interest in that related to the presence of a close binary companion to S106IR, which may produce periodic eclipses or tidal distortion of the shape of the members of the system. Results. A periodic variability of S106IR in the J band is found with a period of 5.0 days and an amplitude of ≃0.1 mag. The light curve displays a slow rise from minimum to maximum followed by a steep decrease, and can be well reproduced by a close binary system composed of two stars with different luminosities orbiting each other in an elliptical orbit of moderate eccentricity. S106IR also shows hints of short-term variability that is possibly related to accretion. We also report variability of four other stars previously classified as members of the S106 cluster, all of which are strong X-ray emitters. Conclusions. The newly discovered close binarity of S106IR adds a new element to the modeling of the nebula and the understanding of the dynamics of the gas around the ionizing source, which suggests that the components of the binary are accreting via a circumbinary disk. Binarity also helps to explain the apparent mismatch between the spectral type of the ionizing source inferred from the nebular spectrum and its high brightness at near-infrared wavelengths.