Novel antimicrobial 3D-printed alginate/bacterial-cellulose hydrogels with in situ-synthesized copper nanostructures were developed having improved printability. Prior to 3D printing, two methods were tested for the development of the alginate hydrogels: (a) ionic cross-linking with calcium ions followed by ion exchange with copper ions (method A) and (b) ionic cross-linking with copper ions (method B). A solution containing sodium borohydride, used as a reducing agent, was subsequently added to the hydrogels, producing in situ clusters of copper nanoparticles embedded in the alginate hydrogel matrix. The method used and concentrations of copper and the reducing agent were found to affect the stability of the alginate/copper hydrogels, with method A producing more stable materials. By increasing the alginate concentration from 1 to 4 wt % and by using method A, alginate/bacterial-cellulose/copper hydrogel structures were 3D-printed having excellent printability as compared with pure alginate hydrogels. It is noteworthy that after reduction with sodium borohydride, the 3D structures presented antimicrobial behavior against Escherichia coli and Staphylococcus aureus strains. Our results introduce a simple route for the production of alginate/cellulose inks with improved behavior toward antimicrobial 3D-printed materials.