Context. Shadows in scattered light images of protoplanetary disks are a common feature and support the presence of warps or misalignments between disk regions. These warps are possibly caused by an inclined (sub-)stellar companion embedded in the disk. Aims. We aim to study the morphology of the protoplanetary disk around the Herbig Ae star HD 139614 based on the first scattered light observations of this disk, which we model with the radiative transfer code MCMax3D. Methods. We obtained J- and H-band observations that show strong azimuthal asymmetries in polarized scattered light with VLT/SPHERE. In the outer disk, beyond ~30 au, a broad shadow spans a range of ~240 deg in position angle, in the east. A bright ring at ~16 au also shows an azimuthally asymmetric brightness, with the faintest side roughly coincidental with the brightest region of the outer disk. Additionally, two arcs are detected at ~34 and ~50 au. We created a simple four-zone approximation to a warped disk model of HD 139614 in order to qualitatively reproduce these features. The location and misalignment of the disk components were constrained from the shape and location of the shadows they cast. Results. We find that the shadow on the outer disk covers a range of position angles too wide to be explained by a single inner misaligned component. Our model requires a minimum of two separate misaligned zones – or a continuously warped region – to cast this broad shadow on the outer disk. A small misalignment of ~4° between adjacent components can reproduce most of the observed shadow features. Conclusions. Multiple misaligned disk zones, potentially mimicking a warp, can explain the observed broad shadows in the HD 139614 disk. A planetary mass companion in the disk, located on an inclined orbit, could be responsible for such a feature and for the dust-depleted gap responsible for a dip in the SED.