The vibrational and anisotropic relaxation dynamics and structural dynamics of a potential anticancer prodrug, trans,trans,trans-[Pt(N3)2(OH)2(py)2], were investigated using time-resolved infrared pump-probe spectroscopy and ultrafast two-dimensional infrared (2D IR) spectroscopy. Herein, two representative bio-friendly solvents, H2O and DMSO, were used, in which the local structural and dynamical variations were monitored using the antisymmetric linear combination of the two N3 stretching vibrational modes as an infrared probe. It was found that the vibrational relaxation process of the N3 antisymmetric stretching (as) mode in H2O is two to three times faster than that in DMSO. The anisotropic relaxation process of the anticancer prodrug was observed to be hindered in DMSO; this indicated a tighter solvent environment around the sample molecule in this solvent. The vibrational frequency time correlation of the N3 antisymmetric stretching mode in H2O decays with a time constant of 1.94 ps, in agreement with the hydrogen bond formation and breaking times of water. In DMSO, the frequency time correlation of the N3 as mode decays on a much longer time scale; this further indicates its sensitivity to the out-layer DMSO structural dynamics, which are relatively static in the experimental time window.