Every year millions of people worldwide undergo surgical interventions, with the occurrence of mild or severe post-treatment consequences meaning that rehabilitation plays a key role in modern medicine. Considering the cases of burns and plastic surgery, the pressing need for new materials that can be used for wound patches or body fillers and are able to sustain tissue regeneration and promote cell adhesion and proliferation is clear. The challenges facing next-generation implant materials also include the need for improved structural properties for cellular organization and morphogenic guidance together with optimal mechanical, rheological, and topographical behavior. Herein, we propose for the first time a sodium alginate hydrogel obtained by a thiol-yne reaction, easily synthesized using carbodiimide chemistry in a two-step reaction. The hydrogels were formed in all cases within a few minutes of light irradiation, showing good self-standing properties under solicitation. The mechanical, rheological, topographical, and swelling properties of the gels were also tested and reported. Lastly, no cytotoxicity was detected among the hydrogels. Soluble extracts in culture media allowed cell proliferation, and no differences between samples were detected in terms of metabolic activity and DNA content. These results suggest the potential use of these cytocompatible hydrogels in tissue engineering and regenerative medicine.