Pd(II)-compounds are presently regarded as promising anticancer drugs, as an alternative to Pt(II)-based drugs (e.g., cisplatin), which typically trigger severe side-effects and acquired resistance. Dinuclear Pd(II) complexes with biogenic polyamines such as spermine (PdSpm) have exhibited particularly beneficial cytotoxic properties, hence unveiling the importance of understanding their impact on organism metabolism. The present study reports the first nuclear magnetic resonance (NMR)-based metabolomics study to assess the impact of PdSpm on the metabolism of healthy mice, to identify metabolic markers with possible relation to biotoxicity/side-effects and their dynamics. The changes in the metabolic profiles of both aqueous and lipophilic extracts of mice kidney, liver, and breast tissues were evaluated, as a function of drug-exposure time, using cisplatin as a reference drug. A putative interpretation was advanced for the metabolic deviations specifically triggered by PdSpm, this compound generally inducing faster metabolic response and recovery to control levels for all organs tested, compared to cisplatin (except for kidney lipid metabolism). These results constitute encouraging preliminary metabolic data suggestive of potential lower negative effects of PdSpm administration.