Herein, we demonstrate the feasibility of a three-dimensional printed chitosan (CS)-poly(vinyl alcohol) (PVA)-gelatin (Gel) hydrogel incorporating the antimicrobial drug levofloxacin (LEV) as a potential tissue engineering scaffold. Hydrogels were prepared by physically cross-linking the polymers, and the printability of the prepared hydrogels was determined. The hydrogel with 3% w/v of CS, 3% w/v of PVA, and 2% w/v of Gel presented the best printability, producing smooth and uniform scaffolds. The integrity of 3D-printed scaffolds was improved via a neutralization process since after testing three different neutralized agents, i.e., NH3 vapors, EtOH/NaOH, and KOH solutions. It was proved that the CS/PVA/Gel hydrogel was formed by hydrogen bonds and remained amorphous in the 3D-printed structures. Drug loading studies confirmed the successful incorporation of LEV, and its in vitro release continued for 48 h. The cytotoxicity/cytocompatibility tests showed that all prepared scaffolds were cytocompatible.