Uncontrolled bleeding causes more than 30% of deaths due to injuries worldwide. Modern hemostatic materials based on synthetic and biological macromolecules focus mainly on the time prior to hemostasis, but the prevention of a bacterial infection is also crucial for increasing survival. Silver is known to exhibit potent antimicrobial activity and strong biocidal effects against various types of bacteria. A new method for producing of composite sponges with a pronounced antimicrobial effect based on such biological polymers as alginate and chitosan with the addition of silver nanoparticles has been proposed. The method is based on the combination of cryostructuring, ionotropic gelation and ion substitution methods during the formation of the macroporous structure of the sponge at the gelation stage with subsequent freeze drying. Silver nanoparticles isolated by three fungal cultures were introduced into the sponges in low concentrations. The alginate–chitosan–composite sponges with Ag nanoparticles showed high sorption capacity, microporous structure and increased antimicrobial activity compared to a composite sponge without the inclusion of silver nanoparticles.