The red swamp crayfish (Procambarus clarkii) is a widely distributed invasive species that is listed in the Delivering Alien Invasive Species Inventory for Europe. Native to North America, it has been introduced to numerous regions, such as the Canary Islands, Spain. Previous studies have confirmed the role of this crayfish in the maintenance of several foodborne pathogenic bacteria. Therefore, the aim of this study was to analyze the main zoonotic bacterial and parasitic pathogens present in a P. clarkii population introduced to the island of Tenerife, Canary Islands, and to assess the potential risk to public health and native fauna. A total of 22 crayfish from Tenerife were analyzed using Biofire FilmArray Gastrointestinal Panels and culture–PCR methods. The results show the presence of Plesiomonas shigelloides, Shigella/enteroinvasive Escherichia coli, enteropathogenic Escherichia coli, Salmonella ser. Enteritidis, Salmonella ser. Typhimurium, and Salmonella ser. Typhi. These results demonstrate the presence of a variety of pathogenic bacteria in the red swamp crayfish in Tenerife that represent a significant concern in terms of public health and conservation. Implementing educational campaigns to inform the community about the risks associated with handling and consuming contaminated crayfish, as well as initiatives for the restoration of the contaminated ecosystem, are necessary to prevent the transmission of the foodborne pathogens.