The high-pressure behavior of technologically important visible-light photocatalytic semiconductor InNbO4, adopting a monoclinic wolframite-type structure at ambient conditions, was investigated using synchrotron-based X-ray diffraction, Raman spectroscopic measurements, and first-principles calculations. The experimental results indicate the occurrence of a pressure-induced isostructural phase transition in the studied compound beyond 10.8 GPa. The large volume collapse associated with the phase transition and the coexistence of two phases observed over a wide range of pressure shows the nature of transition to be first-order. There is an increase in the oxygen anion coordination number around In and Nb cations from six to eight at the phase transition. The ambient-pressure phase has been recovered on pressure release. The experimental pressure-volume data when fitted to a Birch-Murnaghan equation of states yields the value of ambient pressure bulk modulus as 179(2) and 231(4) GPa for the low- and high-pressure phases, respectively. The pressure dependence of the Raman mode frequencies and Grüneisen parameters was determined for both phases by experimental and theoretical methods. The same information is obtained for the infrared modes from first-principles calculations. Results from theoretical calculations corroborate the experimental findings. They also provide information on the compressibility of interatomic bonds, which is correlated with the macroscopic properties of InNbO4.