Room temperature angle-dispersive x-ray diffraction measurements on zircon-type EuVO₄, LuVO₄, and ScVO₄ were performed up to 27 GPa. In all the three compounds we found evidence of a pressure-induced structural phase transformation from zircon to a scheelite-type structure. The onset of the transition is near 8 GPa, but the transition is sluggish and low-pressure and high-pressure phases coexist in a pressure range of about 10 GPa. In EuVO₄ and LuVO₄ a second transition to a M-fergusonite-type phase was found near 21 GPa. The equations of state for the zircon and scheelite phases are also determined. Among the three studied compounds, we found that ScVO₄ is less compressible than EuVO₄ and LuVO₄, being the most incompressible orthovanadate studied to date. The sequence of structural transitions and compressibilities are discussed in comparison with other zircon-type oxides.