Three-dimensional bioprinting has emerged as an attractive technology due to its ability to mimic native tissue architecture using different cell types and biomaterials. Nowadays, cell-laden bioink development or skin tissue equivalents are still at an early stage. The aim of the study is to propose a bioink to be used in skin bioprinting based on a blend of fibrinogen and alginate to form a hydrogel by enzymatic polymerization with thrombin and by ionic crosslinking with divalent calcium ions. The biomaterial ink formulation, composed of 30 mg/mL of fibrinogen, 6% of alginate, and 25 mM of CaCl2, was characterized in terms of homogeneity, rheological properties, printability, mechanical properties, degradation rate, water uptake, and biocompatibility by the indirect method using L929 mouse fibroblasts. The proposed bioink is a homogeneous blend with a shear thinning behavior, excellent printability, adequate mechanical stiffness, porosity, biodegradability, and water uptake, and it is in vitro biocompatible. The fibrinogen-based bioink was used for the 3D bioprinting of the dermal layer of the skin equivalent. Three different normal human dermal fibroblast (NHDF) densities were tested, and better results in terms of viability, spreading, and proliferation were obtained with 4 × 106 cell/mL. The skin equivalent was bioprinted, adding human keratinocytes (HaCaT) through bioprinting on the top surface of the dermal layer. A skin equivalent stained by live/dead and histological analysis immediately after printing and at days 7 and 14 of culture showed a tissuelike structure with two distinct layers characterized by the presence of viable and proliferating cells. This bioprinted skin equivalent showed a similar native skin architecture, paving the way for its use as a skin substitute for wound healing applications.