We have revealed the pressure-induced collapse of the guest Eu off-centering in type-I clathrate Eu8Ga16Ge30 by the measurements of extended X-ray absorption fine structure (EXAFS) at the Ge K-edge in a temperature range of 10-300 K. Our analysis of the EXAFS spectra at ambient pressure confirmed that the guest Eu is located in the off-centered positions Delta(offset) = 0.39(1) angstrom away from the center of the Ga/Ge tetradodecahedron cage (14-cage). However, with applying pressure to 13.1 GPa, Delta(offset) decreases to zero, and the atomic density of Eu is concentrated near the center of the 14-cage with a broad distribution. The present result demonstrates a close relationship between Delta(offset) and the size of the cage Delta(offset) decreases when the 14-cage shrinks by applying pressure. With further compression, we have observed a drastic change in the EXAFS spectra due to amorphization. In the amorphous phase, the first nearest neighbor Ge-Ga/Ge bond is longer than in the crystal phase, whereas the guest Eu atom is located randomly with respect to the Ge atoms.