Hydrogel-based stem cell therapy uses different stem cells and bioactive molecules for wound healing in the treatment of diabetes and chronic burn wounds by accelerating angiogenesis, collagen deposition, and inhibition of inflammatory responses. Artificial vessels have already been used for patients with cardiovascular diseases, but most of them are polymeric, which can cause thrombosis and restenosis. 3D bioprinting combines cells, growth factors, and biomaterials to create a setting in which cells grow and differentiate into native tissue-like structures. The current study aimed to create a model of blood vessels using collagen and hyaluronic acid hydrogel combined with endothelial and muscle progenitor cells derived from amniotic mesenchymal stem cells using 3D bioprinting. A computer-aided design (CAD) software was employed to create the 3D models of a blood vessel model and printed using a 3D bioprinter with two printheads: one with bioink encapsulating endothelial progenitor cells and the second with bioink encapsulating smooth muscle progenitor cells. The blood vessel constructs were characterized morphologically and structurally by Fourier Transform Infrared (FTIR) Spectroscopy, thermogravimetric analysis (TGA), Scanning Electron Microscopy (SEM), immunohistochemistry, water uptake, and enzymatic degradation. Viability, proliferation, oxidative stress, vascular endothelial growth factor (VEGF) and nitric oxide (NO) production were assessed to demonstrate the cytocompatibility of the blood vessel constructs. Our results showed that collagen–hyaluronic acid hydrogels embedded with stem cells can be used for vascular constructs, meeting the desired requirements of biocompatibility and accuracy in reproducing the model created in the CAD software v1.0.