Hydrogel injection molding is a biofabrication method that is useful for the rapid generation of complex cell‐laden hydrogel geometries, with potential utility in biomanufacturing products for tissue engineering applications. Hydrogel injection molding requires that hydrogel polymers have sufficiently delayed crosslinking times to enable injection and molding prior to gelation. In this work, we explore the feasibility of injection molding synthetic poly(ethylene) glycol (PEG)‐based hydrogels functionalized with strain promoted azide‐alkyne cycloaddition click chemistry functional groups. We evaluate the mechanical properties of a PEG‐based hydrogel library, including time to gelation and successful generation of complex geometries via injection molding. We evaluate the binding and retention of adhesive ligand RGD within the library matrices and characterize the viability and function of encapsulated cells. This work demonstrates the feasibility of injection molding synthetic PEG‐based hydrogels for tissue engineering applications, with potential utility in the clinic and biomanufacturing.