Context. While planet formation is thought to occur early in the history of a protoplanetary disk, the presence of planets embedded in disks, or of other processes driving disk evolution, might be traced from their imprints on the disk structure. Aims. We study the morphology of the disk around the T Tauri star HD 143006, located in the ~5–11 Myr-old Upper Sco region, and we look for signatures of the mechanisms driving its evolution. Methods. We observed HD 143006 in polarized scattered light with VLT/SPHERE at near-infrared (J-band, 1.2 μm) wavelengths, reaching an angular resolution of ~0.037′′ (~6 au). We obtained two datasets, one with a 145 mas diameter coronagraph, and the other without, enabling us to probe the disk structure down to an angular separation of ~0.06′′ (~10 au). Results. In our observations, the disk of HD 143006 is clearly resolved up to ~0.5′′ and shows a clear large-scale asymmetry with the eastern side brighter than the western side. We detect a number of additional features, including two gaps and a ring. The ring shows an overbrightness at a position angle (PA) of ~140°, extending over a range in position angle of ~60°, and two narrow dark regions. The two narrow dark lanes and the overall large-scale asymmetry are indicative of shadowing effects, likely due to a misaligned inner disk. We demonstrate the remarkable resemblance between the scattered light image of HD 143006 and a model prediction of a warped disk due to an inclined binary companion. The warped disk model, based on the hydrodynamic simulations combined with three-dimensional radiative transfer calculations, reproduces all major morphological features. However, it does not account for the observed overbrightness at PA ~ 140°. Conclusions. Shadows have been detected in several protoplanetary disks, suggesting that misalignment in disks is not uncommon. However, the origin of the misalignment is not clear. As-yet-undetected stellar or massive planetary companions could be responsible for them, and naturally account for the presence of depleted inner cavities.