Volumetric muscle loss (VML), which involves the loss of a substantial portion of muscle tissue, is one of the most serious acute skeletal muscle injuries in the military and civilian communities. The injured area in VML may be so severely affected that the body loses its innate capacity to regenerate new functional muscles. State-of-the-art biofabrication methods such as bioprinting provide the ability to develop cell-laden scaffolds that could significantly expedite tissue regeneration. Bioprinted cell-laden scaffolds can mimic the extracellular matrix and provide a bioactive environment wherein cells can spread, proliferate, and differentiate, leading to new skeletal muscle tissue regeneration at the defect site. In this study, we engineered alginate−gelatin composite inks that could be used as bioinks. Then, we used the inks in an extrusion printing method to develop design-specific scaffolds for potential VML treatment. Alginate concentration was varied between 4−12% w/v, while the gelatin concentration was maintained at 6% w/v. Rheological analysis indicated that the alginate−gelatin inks containing 12% w/v alginate and 6% w/v gelatin were most suitable for developing high-resolution scaffolds with good structural fidelity. The printing pressure and speed appeared to influence the printing accuracy of the resulting scaffolds significantly. All the hydrogel inks exhibited shear thinning properties and acceptable viscosities, though 8−12% w/v alginate inks displayed properties ideal for printing and cell proliferation. Alginate content, crosslinking concentration, and duration played significant roles (p < 0.05) in influencing the scaffolds’ stiffness. Alginate scaffolds (12% w/v) crosslinked with 300, 400, or 500 mM calcium chloride (CaCl2) for 15 min yielded stiffness values in the range of 45−50 kPa, i.e., similar to skeletal muscle. The ionic strength of the crosslinking concentration and the alginate content significantly (p < 0.05) affected the swelling and degradation behavior of the scaffolds. Higher crosslinking concentration and alginate loading enhanced the swelling capacity and decreased the degradation kinetics of the printed scaffolds. Optimal CaCl2 crosslinking concentration (500 mM) and alginate content (12% w/v) led to high swelling (70%) and low degradation rates (28%) of the scaffolds. Overall, the results indicate that 12% w/v alginate and 6% w/v gelatin hydrogel inks are suitable as bioinks, and the printed scaffolds hold good potential for treating skeletal muscle defects such as VML.