Two novel transitional organic Zn/Cu complexes based on a new biocompatible bidentate triazine–hydrazone ligand (Thz) was designed, synthesized, and evaluated in this study. This study evaluated the effects of injecting 60 mg of Zn and 40 mg of Cu in three different forms, twice per week, for eight weeks on growth performance, expression of growth factors and cytokine genes, carcass yield, blood biochemicals, and intestinal morphology in weaned rabbits. The tested complexes were sulfate (Cu/ZnSO4), montmorillonite (Cu/Zn-Mnt), and triazine hydrazone (Cu/Zn-Thz). A total of 60 V-line weaned rabbits at four weeks of age were assigned to four treatments (n = 15), which were intramuscularly injected with 0.5 mL of either (1) saline (control) or saline containing (2) Cu/ZnSO4, (3) Cu/Zn-Mnt, or (4) Cu/Zn-Thz. Compared to the controls, the rabbits injected with Cu/Zn-Thz showed a higher (p < 0.01) growth rate, carcass yield (p < 0.05), and liver expression of insulin like growth factor-1 (IGF-1), growth hormone receptor (GHR), fibroblast growth factor-1 (FGF1), and transforming growth factor beta-1 (TGFB1) (p < 0.05), as well as better jejunum morphometric variables (p < 0.05). On the other hand, mRNA of FGF1, TGF1, TCIRG1, and adenosine deaminase (ADA) were higher expressed (p < 0.05) in the spleen tissues of Cu/Zn-Mnt group. Collectively, the results indicated that our novel synthesized organic complexes of Zn/Cu-Thz proved to be a suitable feed supplement, as it increased rabbit productive performance through enhancing expression of peptide growth factors and cytokine genes.