In this paper we perform a high-pressure study of fergusonite-type HoNbO4. Powder x-ray diffraction experiments and ab initio density-functional theory simulations provide evidence of a phase transition at 18.9(1.1) GPa from the monoclinic fergusonite-type structure (space group I2/a) to another monoclinic polymorph described by space group P21/c. The phase transition is reversible and the high-pressure structural behavior is different than the one previously observed in related niobates. The high-pressure phase remains stable up to 29 GPa. The observed transition involves a change in the Nb coordination number from 4 to 6, and it is driven by mechanical instabilities. We have determined the pressure dependence of unit-cell parameters of both phases and calculated their room-temperature equation of state. For the fergusonite-phase we have also obtained the isothermal compressibility tensor. In addition to the high-pressure studies, we report ambient-pressure Raman and infrared spectroscopy measurements. We have been able to identify all the active modes of fergusonite-type HoNbO4, which have been assigned based upon density-functional theory calculations. These simulations also provide the elastic constants of the different structures and the pressure dependence of the Raman and infrared modes of the two phases of HoNbO4.