Curcumin (CUR) is a natural substance extracted from turmeric that has antimicrobial properties. Due to its ability to absorb light in the blue spectrum, CUR is also used as a photosensitizer (PS) in antimicrobial Photodynamic Therapy (aPDT). However, CUR is hydrophobic, unstable in solutions, and has low bioavailability, which hinders its clinical use. To circumvent these drawbacks, drug delivery systems (DDSs) have been used. In this review, we summarize the DDSs used to carry CUR and their antimicrobial effect against viruses, bacteria, and fungi, including drug-resistant strains and emergent pathogens such as SARS-CoV-2. The reviewed DDSs include colloidal (micelles, liposomes, nanoemulsions, cyclodextrins, chitosan, and other polymeric nanoparticles), metallic, and mesoporous particles, as well as graphene, quantum dots, and hybrid nanosystems such as films and hydrogels. Free (non-encapsulated) CUR and CUR loaded in DDSs have a broad-spectrum antimicrobial action when used alone or as a PS in aPDT. They also show low cytotoxicity, in vivo biocompatibility, and improved wound healing. Although there are several in vitro and some in vivo investigations describing the nanotechnological aspects and the potential antimicrobial application of CUR-loaded DDSs, clinical trials are not reported and further studies should translate this evidence to the clinical scenarios of infections.