Herein, we report a new Cu(II) complex [Cu(L)(2,2′‐bipy)](ClO4) obtained from a N,N,O donor Schiff base ligand, 2‐methoxy‐6‐((piperidin‐2‐ylmethylimino)methyl)phenol (HL), and 2,2′‐bipyridine. The title complex has been characterized using FTIR, electronic (UV–Vis), electrospray ionization mass spectrometry (ESI‐MS), and single‐crystal X‐ray studies. The crystallographic studies support the chemical formula, [Cu(L)(2,2′‐bipy)](ClO4), where the metal is coordinated by the deprotonated ligand L through N,N,O atoms and by a 2,2′‐bipy molecule chelating through the N donors. Thus, the studied complex attains penta‐coordinated distorted square pyramidal geometry with ON4 atomic environment. The existence of various non‐covalent interactions such as van der Waals, hydrogen bonding, and hydrophobic interactions that are very common in protein–small molecule interaction has been identified in the present complex from Hirshfeld surface analysis. This has provoked us to examine the nature of interactions of the studied complex with DNA and BSA protein by combined theoretical and experimental approaches. The experimental results reveal the strong binding ability of the complex to CT‐DNA by the mode of partial intercalation and to BSA by the hydrophobic manner. Apart from this, the molecular docking methodology that is used as theoretical tool in the present study also supports the binding ability and binding site of the complex inside the DNA and BSA protein. Moreover, cytotoxicity of the complex has been checked against SiHa cancer cell representing the biocompatibility of the complex and signifying its use as biomaterial transplant.