In pursue of a systematic characterization of rare-earth vanadates under compression, in this work we have studied the phase behavior of zircon-type orthovanadate PrVO$_4$ under high pressure conditions, up to 24 GPa, by means of powder x-ray diffraction. We have found that PrVO$_4$ undergoes a zircon to monazite transition around 6 GPa, confirming previous results found on Raman experiments. A second transition takes place above 14 GPa, to a BaWO$_4$-II -type structure. The zircon to monazite structural sequence is an irreversible first-order transition, accompanied by a volume collapse of about 9.6%. Monazite phase is thus a metastable polymorph of PrVO$_4$. The monazite- BaWO$_4$-II transition is found to be reversible instead and occurs with a similar volume change. Here we report on the axial and bulk compressibility of all phases. We also compare our results with those for other rare-earth orthovanadates. Finally, by means of optical-absorption experiments and resistivity measurements we determined by the first time the effect of pressure in the electronic properties of PrVO$_4$. We found that the zircon-monazite transition produces a collapse of the band gap and an abrupt decrease of the resistivity. Reasons for this behavior are going to be discussed.