DI Cha A is K0-type pre-main-sequence star, the brightest component of a quadruple stellar system. Here we report on a detailed study of this star based on archival VLTI/MIDI and VLTI/PIONIER infrared interferometric observations, as well as optical-infrared photometric monitoring from ground-based and space-born instruments. We determined the structure of the circumstellar disk by fitting simultaneously the interferometric visibilities and the spectral energy distribution, using both analytical models and the radiative transfer code RADMC-3D. The modeling revealed that the radial density distribution of the disk appears to have a gap between 0.21 and 3.0 au. The inner ring, whose inner size coincides with the sublimation radius, is devoid of small, submicrometer-sized dust grains. The inner edge of the outer disk features a puffed-up rim, typically seen in intermediate-mass stars. Grain growth, although less progressed, was also detected in the outer disk. The inner ring is variable at mid-infrared wavelengths on both daily and annual timescales, while the star stays remarkably constant in the optical, pointing to geometrical or accretion changes in the disk as possible explanations for the flux variations.