It is widely agreed that microbial biofilms play a major role in promoting infection and delaying healing of chronic wounds. In the era of microbial resistance, probiotic strains or their metabolic products are emerging as an innovative approach for the treatment of hard-to-heal (chronic) wounds due to their antimicrobial, healing, and host immune-modulatory effects. In this study, we aimed to investigate the potential of cell-free supernatants (CFS) from Lacticaseibacillus rhamnosus GG against mono- and dual-species biofilms of wound pathogens in a 3D in vitro infection model. Mature biofilms of Pseudomonas aeruginosa and Staphylococcus aureus were obtained on collagen scaffolds in the presence of a simulant wound fluid (SWF) and treated with CFS at different doses and time intervals. At 1:4 dilution in SWF, CFS caused a marked reduction in the colony forming-unit (CFU) numbers of bacteria embedded in mono-species biofilms as well as bacteria released by the biofilms in the supernatant. CFU count and electron microscopy imaging also demonstrated a marked antibiofilm effect against dual-species biofilms starting from 8 h of incubation. Furthermore, CFS exhibited acceptable levels of cytotoxicity at 24 h of incubation against HaCaT cells and, differently from ciprofloxacin, failed to induce resistance after 15 passages at sub-inhibitory concentrations. Overall, the results obtained point to L. rhamnosus GG postbiotics as a promising strategy for the treatment of wound biofilms.