Osteosarcoma cancers are becoming more common in children and young adults, and existing treatments have low efficacy and a very high mortality rate, making it pressing to search for new chemotherapies with high efficacy and high selectivity index. Copper complexes have shown promise in the treatment of osteosarcoma. Here, we report the synthesis, characterization, and anticancer activity of [Cu(N-N-Fur)(NO3)(H2O)] complex where N-N-Fur is (E)-N'-(2-hydroxy-3-methoxybenzylidene)furan-2-carbohydrazide. The [Cu(N-N-Fur)(NO3)(H2O)] complex was characterized via X-ray diffraction and electron spin resonance (ESR), displaying a copper center in a nearly squared pyramid environment with the nitrate ligand acting as a fifth ligand in the coordination sphere. We observed that [Cu(N-N-Fur)(NO3)(H2O)] binds to DNA in an intercalative manner. Anticancer activity on the MG-63 cell line was evaluated in osteosarcoma monolayer (IC50 2D: 1.1 ± 0.1 μM) and spheroids (IC50 3D: 16.3 ± 3.1 μM). Selectivity assays using nontumoral fibroblast (L929 cell line) showed that [Cu(N-N-Fur)(NO3)(H2O)] has selectivity index value of 2.3 compared to cis-diamminedichloroplatinum(II) (CDDP) (SI = 0.3). Additionally, flow cytometry studies demonstrated that [Cu(N-N-Fur)(NO3)(H2O)] inhibits cell proliferation and conveys cells to apoptosis. Cell viability studies of MG-63 spheroids (IC50 = 16.3 ± 3.1 μM) showed that its IC50 value is 4 times lower than for CDDP (IC50 = 65 ± 6 μM). Besides, we found that cell death events mainly occurred in the center region of the spheroids, indicating efficient transport to the microtumor. Lastly, the complex showed dose-dependent reductions in spheroid cell migration from 7.5 to 20 μM, indicating both anticancer and antimetastatic effects.