Hydrogels are widely used as implantable scaffolds and drug delivery carriers for biomedical applications. In particular, in situ cross-linkable hydrogels synthesized via enzyme-mediated reaction have received great attention in the field of injectable biomedical research as they have applications in minimally invasive procedures and have easily controllable physicochemical properties (e.g., gelation time, mechanical properties, etc.) under mild conditions. In this study, we synthesized poly(ethylene glycol) (PEG)-co-polymerized poly(glycerol sebacate) (PGS) polymers (PEG-co-PGS) capable of dissolving in aqueous environments and developed injectable hydrogel platforms via a horseradish peroxidase (HRP)-catalyzed cross-linking reaction. To induce in situ gelling, HRP-reactive phenol moieties (tyramine) were covalently conjugated to the PEG-co-PGS polymers, and hydrogel networks were formed in the presence of HRP and hydrogen peroxide (H2O2). The chemical structures of synthesized polymers were confirmed by 1H-NMR spectroscopy, and the physicochemical properties of the hydrogels were assessed under varying concentrations of HRP and H2O2 solutions. The gelation time of PEG-co-PGS hydrogels ranged from 12 s to 237 s based on the HRP concentration (0.02–0.25 mg/mL), and the elastic modulus (16–41 Pa) depended on H2O2 concentration. In vitro cytocompatibility studies in human dermal fibroblasts revealed that PEG-co-PGS hydrogels were highly cytocompatible, with no negative effects on cell morphology and viability. In conclusion, our results suggest that PGS-based injectable hydrogels with multi-tunable properties and good cytocompatibility have tremendous potential as injectable scaffolds for tissue engineering applications.