We have studied the structural transformation of Sm@C88 under pressure up to 18 GPa by infrared spectroscopy combined with theoretical simulations. The infrared-active vibrational modes of Sm@C88 at ambient conditions have been assigned for the first time. Pressure-induced blue and red shifts of the corresponding vibrational modes indicate an anisotropic deformation of the carbon cage upon compression. We propose that the carbon cage changes from ellipsoidal to approximately spherical around 7 GPa. A smaller deformation of the carbon bonds in the area close to the Sm atom in the cage suggests that the trapped Sm atom plays a role in minimizing the compression of the adjacent bonds. Pressure induced a significant reduction of the band gap of the crystal. The HOMO-LUMO gap of the Sm@C88 molecule decreases remarkably at 7 GPa as the carbon cage is deformed. Also, compression enhances intermolecular interactions and causes a widening of the energy bands. Both effects decrease the band gap of the sample. The carbon cage deforms significantly above 7 GPa, from spherical to a peanut-like shape and collapses at 18 GPa.