The current study developed a drug delivery system through the green chemistry-based synthesis of a biologically friendly metal-organic framework (bio-MOF) called Asp-Cu, which included copper ions and the environmentally friendly molecule L(+)-aspartic acid (Asp). For the first time, diclofenac sodium (DS) was loaded onto the synthesized bio-MOF simultaneously. The system's efficiency was then improved by encapsulating it with sodium alginate (SA). FT-IR, SEM, BET, TGA, and XRD analyses confirmed that DS@Cu-ASP was successfully synthesized. DS@Asp-Cu was found to release the total load within 2 h when used with simulated stomach media. This challenge was overcome by coating DS@Cu-ASP with SA (SA@DS@Cu-ASP). SA@DS@Cu-ASP displayed limited drug release at pH 1.2, and a higher percentage of the drug was released at pH 6.8 and 7.4 due to the pH-responsive nature of SA. In vitro cytotoxicity screening showed that SA@DS@Cu-ASP could be an appropriate biocompatible carrier with >90% cell viability. The on-command drug carrier was observed to be more applicable biocompatible with lower toxicity, as well as adequate loading properties and responsiveness, indicating its applicability as a feasible drug carrier with controlled release.