Two nickel(II) coordination complexes [Ni(L)]₂(1) and [Ni(L)]_n(2) of a tetradentate Schiff base ligand (H₂L) derived from 2-hydroxy-1-naphthaldehyde with ethylenediamine were synthesized, designed, and characterized via spectroscopic and single crystal XRD analyses. Both nickel(II) complexes exhibited unusual Ni⋯Ni interactions and were fully characterized via single-crystal X-ray crystallography. Nickel(II) complexes [Ni(L)]₂(1) and [Ni(L)]_n(2) crystallize in monoclinic and triclinic crystal systems with P2₁/c and P space groups, respectively, and revealed square planar geometry around each Ni(II) ion. The structure of both the complexes have established the existence of a new kind of metal system containing nickel(II)–nickel(II) interactions with a square planar-like geometry about the nickel(II) atoms. Both square planar Ni(II) complexes were often stacked with relatively short Ni⋯Ni distances. The non-bonded Ni–Ni distance (Ni⋯Ni separation) seems to be 3.356 Å and 3.214 Å from the nickel atoms of [Ni(L)]₂(1) and [Ni(L)]_n(2), respectively. These distances are shorter than the sum of their van der Waals radii (4.80 Å) but longer than the sum of their covalent radii (2.50 Å), indicating that there is a Ni⋯Ni interaction but not a Ni–Ni bond. The discrete molecules are π-stacked and connected via weak intermolecular interactions (C–H⋯O and C–H⋯N). Cyclic voltammetry measurements were obtained for both the complexes, and their pharmacokinetic and chemoinformatics properties were also explored. Detailed structural analysis and non-covalent supramolecular interactions were investigated using single-crystal structure analysis and computational approaches. Both the unique structures show good inhibition performance for the Omicron spike proteins of the SARS CoV-2 virus. To gain insights into potential SARS-CoV-2 Omicron drugs and find inhibitors against the Omicron variants of SARS-CoV-2, we examined the molecular docking of the nickel(II) complexes [Ni(L)]₂(1) and [Ni(L)]_n(2) with the SARS-CoV-2 Omicron spike protein (PDB ID: 7WK2 and 7WVO). A strong binding was predicted between Ni(II) coordination complexes [Ni(L)]₂(1) and [Ni(L)]_n(2) with the SARS-CoV-2 Omicron variant receptor protein through the negative value of binding affinity. Molecular docking of Nil(II) complexes [Ni(L)]₂(1) and [Ni(L)]_n(2) with a DNA duplex (PDB ID: 7D3T) and RNA (PDB ID: 7TDC) binding protein was also studied. Overall, this study suggests that Ni(II) complexes can be considered as drug candidates against the Omicron variants of SARS-CoV-2.