Wound care devices having a topically applied silver-based antimicrobial finish are provided. The finish comprises at least one silver ion-containing compound and at least one binder compound. The finish may be applied to a target substrate, such as a fiber, fabric, film, foam, hydrogel, or hydrocolloid to provide a single layer antimicrobial wound care device. Alternatively, a silver-containing layer may be combined with one or more additional layers of target substrate to provide a composite antimicrobial wound care device. The device may also contain an odor-absorbing component capable of reducing or eliminating odors that are inherently associated with infectious wounds. Also provided is a method for making the wound care device and a composition of matter comprising the silver-based antimicrobial finish.