ABSTRACT Misalignments within protoplanetary discs are now commonly observed, and features such as shadows in scattered light images indicate departure from a co-planar geometry. VLT/SPHERE (Very Large Telescope/Spectro-Polarimetric High-​contrast Exoplanet REsearch) observations of the disc around HD 143006 show a large-scale asymmetry and two narrow dark lanes that are indicative of shadowing. ALMA (Atacama Large Millimeter/submillimeter Array) observations also reveal the presence of rings and gaps in the disc, along with a bright arc at large radii. We present new hydrodynamic simulations of HD 143006, and show that a configuration with both a strongly inclined binary and an outer planetary companion is the most plausible to explain the observed morphological features. We compute synthetic observations from our simulations, and successfully reproduce both the narrow shadows and the brightness asymmetry seen in infrared scattered light. Additionally, we reproduce the large dust observed in the mm continuum, due to a 10 Jupiter-mass planet detected in the CO kinematics. Our simulations also show the formation of a circumplanetary disc, which is misaligned with respect to the outer disc. The narrow shadows cast by the inner disc and the planet-induced ‘kink’ in the disc kinematics are both expected to move on a time-scale of ∼5–10 yr, presenting a potentially observable test of our model. If confirmed, HD 143006 would be the first known example of a circumbinary planet on a strongly misaligned orbit.